{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 4. Semi-supervised EM"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## (a) Convergence\n",
    "\n",
    "We saw in the lecture that for \n",
    "$$J(Q,\\theta):= \\sum_{i=1}^m \\sum_{z^{(i)}} Q_i(z^{(i)}) \\log \\frac{p(x^{(i)},z^{(i)};\\theta)}{Q_i(z^{(i)})},$$\n",
    "where $Q$ is any set of distributions $Q_i$, we have the inequality"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$ \\ell_\\text{unsup}(\\theta) \\geq J(Q,\\theta),$$\n",
    "in which equality holds iff \n",
    "$$ Q_i(z^{(i)}) = p(z^{(i)}\\mid x^{(i)};\\theta).$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using $J$ we can rewrite $\\theta^{(t+1)}$ as \n",
    "$$ \\theta^{(t+1)} = \\arg\\max_\\theta \\left[J(Q^{(t)}, \\theta) + \\alpha \\ell_\\text{sup}(\\theta)\\right].$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Therefore\n",
    "$$\\begin{align*}\n",
    "\\ell_\\text{semi-sup}(\\theta^{(t)}) &= \\ell_\\text{unsup}(\\theta^{(t)})+\\alpha \\ell_\\text{sup}(\\theta^{(t)})\\\\\n",
    "&= J(Q^{(t)}, \\theta^{(t)}) + \\alpha \\ell_\\text{sup}(\\theta^{(t)})\\\\\n",
    "&\\leq  J(Q^{(t)}, \\theta^{(t+1)}) + \\alpha \\ell_\\text{sup}(\\theta^{(t+1)})\\\\\n",
    "&\\leq \\ell_\\text{unsup}(\\theta^{(t+1)})+\\alpha \\ell_\\text{sup}(\\theta^{(t+1)})\\\\\n",
    "&=\\ell_\\text{semi-sup}(\\theta^{(t+1)}).\n",
    "\\end{align*}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Semi-supervised GMM\n",
    "\n",
    "## (b) Semi-supervised E-Step"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the E-Step we need to re-estimate the distributions of the latent variables $z^{(1)},\\ldots, z^{(m)}$ with our current estimations $\\mu=\\mu^{(t)},\\Sigma=\\Sigma^{(t)},\\phi=\\phi^{(t)}$, i.e. we compute "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\begin{align*}\n",
    "w_j^{(i)}:&= Q_i(z^{(i)}=j)\\\\\n",
    "&= p(z^{(i)}=j \\mid x^{(i)};\\mu,\\Sigma, \\phi)\\\\\n",
    "&= \\frac{p(x^{(i)}\\mid z^{(i)}=j;\\mu_j,\\Sigma_j)p(z^{(i)}=j;\\phi)}{\\sum_{l=1}^k p(x^{(i)}\\mid z^{(i)}=l;\\mu_l, \\Sigma_l)p(z^{(i)}=l;\\phi)}\n",
    "\\end{align*}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "for $i\\in \\{1,\\ldots, m\\}$ and $j\\in \\{1,\\ldots, k\\}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plugging in\n",
    "$$\\begin{align*}\n",
    "p(z^{(i)}=l;\\phi)&=\\phi_l,\\\\\n",
    "p(x^{(i)}\\mid z^{(i)}=l;\\mu_l,\\Sigma_l) &= (2\\pi)^{-\\frac n2}|\\Sigma_l|^{-\\frac 1 2}\\exp\\left(-\\frac 1 2 (x^{(i)}-\\mu_l)^T\\Sigma_l^{-1}(x^{(i)}-\\mu_l)\\right)\n",
    "\\end{align*}$$\n",
    "this simplifies to"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\begin{align*}\n",
    "w_j^{(i)} &= \\frac{|\\Sigma_j|^{-\\frac 1 2}\\exp\\left(-\\frac 1 2 (x^{(i)}-\\mu_j)^T\\Sigma_j^{-1}(x^{(i)}-\\mu_j)\\right)\\phi_j}{\\sum_{l=1}^k |\\Sigma_l|^{-\\frac 1 2}\\exp\\left(-\\frac 1 2 (x^{(i)}-\\mu_l)^T\\Sigma_l^{-1}(x^{(i)}-\\mu_l)\\right)\\phi_l}.\n",
    "\\end{align*}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## (c) Semi-supervised M-Step\n",
    "\n",
    "In the M-step we reestimate the model parameters $\\mu,\\Sigma,\\phi$ by setting"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\begin{align*}\n",
    "(\\mu^{(t+1)},\\Sigma^{(t+1)},\\phi^{(t+1)}):=\\arg\\max_{(\\mu,\\Sigma,\\phi)}&\\sum_{i=1}^m\\sum_{j=1}^k w_j^{(i)}\\log \\frac{p(x^{(i)},z^{(i)}=j;\\mu, \\Sigma,\\phi)}{w_j^{(i)}} \\\\\n",
    "&+ \\alpha \\sum_{i=1}^{\\tilde m}\\log p(\\tilde x^{(i)},\\tilde z^{(i)};\\mu,\\Sigma,\\phi),\n",
    "\\end{align*}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "where \n",
    "$$\\begin{align*}\n",
    "p(x,z;\\mu,\\Sigma,\\phi) &= p(x\\mid z;\\mu_z,\\Sigma_z)p(z;\\phi)\\\\\n",
    "&= (2\\pi)^{-\\frac n2}|\\Sigma_z|^{-\\frac 1 2}\\exp\\left(-\\frac 1 2 (x-\\mu_z)^T\\Sigma_z^{-1}(x-\\mu_z)\\right)\\phi_z.\n",
    "\\end{align*}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With some simplifications this means we are trying to maximize\n",
    "$$\n",
    "\\sum_{i=1}^m\\sum_{j=1}^k w_j^{(i)}\\left(-\\frac 1 2\\log |\\Sigma_j|-\\frac 1 2(x^{(i)}-\\mu_j)^T\\Sigma_j^{-1}(x^{(i)}-\\mu_j)+\\log \\phi_j\\right)\\\\\n",
    "+\\alpha\\sum_{i=1}^{\\tilde m}\\sum_{j=1}^k 1\\{\\tilde z^{(i)} =j\\}\\left(-\\frac 1 2\\log |\\Sigma_j|-\\frac 1 2(\\tilde x^{(i)}-\\mu_j)^T\\Sigma_j^{-1}(\\tilde x^{(i)}-\\mu_j)+\\log \\phi_j\\right).\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Taking the gradient with respect to $\\mu_j$ (for a fixed $j$) gives the equation\n",
    "$$ \\sum_{i=1}^m w_j^{(i)}\\Sigma_j^{-1}(x^{(i)}-\\mu_j^{(t+1)}) + \\alpha \\sum_{i=1}^{\\tilde m}1\\{\\tilde z^{(i)}=j\\} \\Sigma_j^{-1}(x^{(i)}-\\mu_j^{(t+1)}) = 0 $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "from which we conclude \n",
    "$$ \\mu_j^{(t+1)} = \\frac{\\sum_{i=1}^m w_j^{(i)}x^{(i)}+ \\alpha \\sum_{i=1}^{\\tilde m}1\\{\\tilde z^{(i)}=j\\} x^{(i)}}{\\sum_{i=1}^m w_j^{(i)} + \\alpha \\sum_{i=1}^{\\tilde m}1\\{\\tilde z^{(i)}=j\\} }.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To avoid having to compute the derivative of matrix inversion, let's introduce $X_j:=\\Sigma_j^{-1}$ and note that $\\log |\\Sigma_j| = -\\log|X_j|$.\n",
    "\n",
    "Recall that the differential of the determinant function $X\\mapsto |X|$ at $X_j$ evaluated at some matrix $V$ is given by \n",
    "$$ (\\mathrm{d}_{X=X_j}|X|)V=|X_j|\\text{tr}(X_j^{-1}V) = |X_j|\\text{tr}(\\Sigma_j V).$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Therefore\n",
    "$$(\\mathrm{d}_{X=X_j}\\log|X|)V = \\text{tr}(\\Sigma_j V).$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can compute the differential of the term we are trying to maximize with respect to $X_j$, and set it to $0$ to get \n",
    "$$\\begin{align*}\n",
    "0 &= \\sum_{i=1}^m w_j^{(i)}\\left(\\frac 1 2\\text{tr}(\\Sigma_j^{(t+1)} V)-\\frac 1 2(x^{(i)}-\\mu_j)^TV(x^{(i)}-\\mu_j)\\right)\\\\\n",
    "&\\phantom{=} +\\alpha\\sum_{i=1}^{\\tilde m}1\\{\\tilde z^{(i)} =j\\}\\left(\\frac 1 2\\text{tr}(\\Sigma_j^{(t+1)} V)-\\frac 1 2(\\tilde x^{(i)}-\\mu_j)^T V(\\tilde x^{(i)}-\\mu_j)\\right).\n",
    "\\end{align*}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that \n",
    "$$(x^{(i)}-\\mu_j)^TV(x^{(i)}-\\mu_j) = \\text{tr} \\left((x^{(i)}-\\mu_j)(x^{(i)}-\\mu_j)^T V\\right). $$\n",
    "because a scalar ($1\\times 1$-matrix) is its own trace and the trace is cyclic: $\\text{tr} (ABC) = \\text{tr} (CAB)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We find that \n",
    "$$\\begin{align*}\n",
    "\\text{tr}\\left(\\Sigma_j^{(t+1)} V\\right) &= \\text{tr}\\Big(\\Big(\\sum_{i=1}^m w_j^{(i)}(x^{(i)}-\\mu_j)(x^{(i)}-\\mu_j)^T \\\\\n",
    "&\\qquad+\\alpha\\sum_{i=1}^{\\tilde m}1\\{\\tilde z^{(i)} =j\\}(\\tilde x^{(i)}-\\mu_j)(\\tilde x^{(i)}-\\mu_j)^T\\Big)V\\Big)\\\\\n",
    "&\\phantom = \\cdot \\left(\\sum_{i=1}^m w_j^{(i)}+\\alpha\\sum_{i=1}^{\\tilde m}1\\{\\tilde z^{(i)} =j\\}\\right)^{-1}.\n",
    "\\end{align*}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Because this has to hold for all $V$, we conclude\n",
    "$$ \\begin{align*}\n",
    "\\Sigma_j^{(t+1)} = &\\frac{\\sum_{i=1}^m w_j^{(i)}(x^{(i)}-\\mu_j)(x^{(i)}-\\mu_j)^T +\\alpha\\sum_{i=1}^{\\tilde m}1\\{\\tilde z^{(i)} =j\\}(\\tilde x^{(i)}-\\mu_j)(\\tilde x^{(i)}-\\mu_j)^T}{\\sum_{i=1}^m w_j^{(i)}+\\alpha\\sum_{i=1}^{\\tilde m}1\\{\\tilde z^{(i)} =j\\}}.\n",
    "\\end{align*}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally to compute $\\phi^{(t+1)}$ we have to maximize\n",
    "$$ \\sum_{i=1}^m\\sum_{j=1}^k w_j^{(i)}\\log \\phi_j\n",
    "+\\alpha\\sum_{i=1}^{\\tilde m}\\sum_{j=1}^k 1\\{\\tilde z^{(i)} =j\\}\\log \\phi_j $$\n",
    "under the constraint $\\sum_{j=1}^k\\phi_j = 1$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For this consider the Lagrangian\n",
    "$$ \\mathcal L (\\phi, \\lambda) =\\sum_{i=1}^m\\sum_{j=1}^k w_j^{(i)}\\log \\phi_j\n",
    "+\\alpha\\sum_{i=1}^{\\tilde m}\\sum_{j=1}^k 1\\{\\tilde z^{(i)} =j\\}\\log \\phi_j \n",
    "+\\lambda \\left(\\sum_{j=1}^k\\phi_j - 1\\right).$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Differentiating gives \n",
    "$$\\begin{align*}\n",
    "0&= \\frac{\\partial \\mathcal L(\\phi,\\lambda)}{\\partial \\phi_j}\\\\\n",
    "&=\\sum_{i=1}^m w_j^{(i)}\\frac 1 {\\phi_j}\n",
    "+\\alpha\\sum_{i=1}^{\\tilde m} 1\\{\\tilde z^{(i)} =j\\}\\frac 1{\\phi_j} \n",
    "+\\lambda.\n",
    "\\end{align*}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Therefore \n",
    "$$ \n",
    "\\phi_j^{(t+1)} = \\frac{\\sum_{i=1}^m w_j^{(i)}\n",
    "+\\alpha\\sum_{i=1}^{\\tilde m} 1\\{\\tilde z^{(i)} =j\\}} {-\\lambda}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With $\\sum_{j=1}^k\\phi_j = 1$ we can find $\\lambda$, which then gives us\n",
    "$$ \\begin{align*}\n",
    "\\phi_j ^{(t+1)}&= \\frac{\\sum_{i=1}^m w_j^{(i)}\n",
    "+\\alpha\\sum_{i=1}^{\\tilde m} 1\\{\\tilde z^{(i)} =j\\}} \n",
    "{\\sum_{l=1}^k \\left(\\sum_{i=1}^m w_l^{(i)}\n",
    "+\\alpha\\sum_{i=1}^{\\tilde m} 1\\{\\tilde z^{(i)} =l\\}\\right)}\\\\\n",
    "&= \\frac{\\sum_{i=1}^m w_j^{(i)}\n",
    "+\\alpha\\sum_{i=1}^{\\tilde m} 1\\{\\tilde z^{(i)} =j\\}} \n",
    "{m+\\alpha\\tilde m}.\n",
    "\\end{align*}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To summarize:\n",
    "$$\\begin{align*}\n",
    "\\mu_j^{(t+1)} &= \\frac{\\sum_{i=1}^m w_j^{(i)}x^{(i)}+ \\alpha \\sum_{i=1}^{\\tilde m}1\\{\\tilde z^{(i)}=j\\} x^{(i)}}{\\sum_{i=1}^m w_j^{(i)} + \\alpha \\sum_{i=1}^{\\tilde m}1\\{\\tilde z^{(i)}=j\\} },\\\\\n",
    "\\Sigma_j^{(t+1)} &= \\frac{\\sum_{i=1}^m w_j^{(i)}(x^{(i)}-\\mu_j)(x^{(i)}-\\mu_j)^T +\\alpha\\sum_{i=1}^{\\tilde m}1\\{\\tilde z^{(i)} =j\\}(\\tilde x^{(i)}-\\mu_j)(\\tilde x^{(i)}-\\mu_j)^T}{\\sum_{i=1}^m w_j^{(i)}+\\alpha\\sum_{i=1}^{\\tilde m}1\\{\\tilde z^{(i)} =j\\}},\\\\\n",
    "\\phi_j ^{(t+1)}&=\\frac{\\sum_{i=1}^m w_j^{(i)}\n",
    "+\\alpha\\sum_{i=1}^{\\tilde m} 1\\{\\tilde z^{(i)} =j\\}} \n",
    "{m+\\alpha\\tilde m}.\n",
    "\\end{align*}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With $\\alpha=0$ we can recover the formulas for the unsupervised EM-algorithm from the lecture."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## (d) Classical (Unsupervised) EM Implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import os\n",
    "\n",
    "PLOT_COLORS = ['red', 'black', 'blue', 'orange']  # Colors for your plots\n",
    "K = 4           # Number of Gaussians in the mixture model\n",
    "NUM_TRIALS = 3  # Number of trials to run (can be adjusted for debugging)\n",
    "UNLABELED = -1  # Cluster label for unlabeled data points (do not change)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Main function to train models and plot their class assignments:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def main(is_semi_supervised, trial_num):\n",
    "    \"\"\"Problem 3: EM for Gaussian Mixture Models (unsupervised and semi-supervised)\"\"\"\n",
    "    print('Running {} EM algorithm...'\n",
    "          .format('semi-supervised' if is_semi_supervised else 'unsupervised'))\n",
    "\n",
    "    # Load dataset\n",
    "    train_path = os.path.join('data', 'ds3_train.csv')\n",
    "    x, z = load_gmm_dataset(train_path)\n",
    "    x_tilde = None\n",
    "\n",
    "    if is_semi_supervised:\n",
    "        # Split into labeled and unlabeled examples\n",
    "        labeled_idxs = (z != UNLABELED).squeeze()\n",
    "        x_tilde = x[labeled_idxs, :]   # Labeled examples\n",
    "        z = z[labeled_idxs, :]         # Corresponding labels\n",
    "        x = x[~labeled_idxs, :]        # Unlabeled examples\n",
    "\n",
    "    # *** START CODE HERE ***\n",
    "    m,n = x.shape\n",
    "    # (1) Initialize mu and sigma by splitting the m data points uniformly at random\n",
    "    # into K groups, then calculating the sample mean and covariance for each group\n",
    "    classes = np.random.randint(K, size=m)\n",
    "    \n",
    "    # shape (k,n)\n",
    "    mu = np.array([x[classes == j].mean(axis=0) for j in range(K)])\n",
    "    #print(mu.shape, \"mu shape\", \"want:\", (K,n))\n",
    "    sigma = []\n",
    "    for j in range(K):\n",
    "        class_size = (classes == j).sum()\n",
    "        \n",
    "        # shape (class_size,n)\n",
    "        xj_normed = x[classes ==j]-mu[j] \n",
    "        \n",
    "        # shape (n,n)\n",
    "        sigma.append(xj_normed.T @ xj_normed /class_size)\n",
    "        \n",
    "\n",
    "    \n",
    "    # (2) Initialize phi to place equal probability on each Gaussian\n",
    "    # phi should be a numpy array of shape (K,)\n",
    "    phi = np.ones((K,))/K\n",
    "    # (3) Initialize the w values to place equal probability on each Gaussian\n",
    "    # w should be a numpy array of shape (m, K)\n",
    "    w = np.ones((m, K))/K\n",
    "    # *** END CODE HERE ***\n",
    "\n",
    "    if is_semi_supervised:\n",
    "        w = run_semi_supervised_em(x, x_tilde, z, w, phi, mu, sigma)\n",
    "    else:\n",
    "        w = run_em(x, w, phi, mu, sigma)\n",
    "\n",
    "    # Plot your predictions\n",
    "    z_pred = np.zeros(m)\n",
    "    if w is not None:  # Just a placeholder for the starter code\n",
    "        for i in range(m):\n",
    "            z_pred[i] = np.argmax(w[i])\n",
    "\n",
    "    plot_gmm_preds(x, z_pred, is_semi_supervised, plot_id=trial_num)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Helper function to compute the joint distribution $p(x,z;\\phi, \\mu,\\Sigma)$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def joint_pdf(x, phi, mu, sigma, with_supervision=False, x_tilde=None, z=None):\n",
    "    \"\"\"\n",
    "    Args:\n",
    "        x: Design matrix of shape (m, n).\n",
    "        phi: mixture prior, of shape (k,).\n",
    "        mu: cluster means, list of k arrays of shape (n,).\n",
    "        sigma: cluster covariances, list of k arrays of shape (n, n).\n",
    "        \n",
    "        optional for semi-supervised case:\n",
    "        with_supervision: boolean\n",
    "        x_tilde: Design matrix of shape (m_tilde, n)\n",
    "        z: observed values, shape (m_tilde,1)\n",
    "\n",
    "    Returns: \n",
    "        in unsupervised case:\n",
    "        joint pdf p(x,z; phi, mu, sigma), array of shape (m,k)\n",
    "        \n",
    "        in semisupervised case also returns\n",
    "        joint pdf p(x_tilde, z; phi, mu, sigma), array of shape (m_tilde,)\n",
    "    \"\"\"\n",
    "    m,n = x.shape\n",
    "    k,= phi.shape\n",
    "    \n",
    "    # compute determinants and inverses of the covariance matrices\n",
    "    det_sigma = np.linalg.det(sigma) #shape (k,)\n",
    "    inv_sigma = np.linalg.inv(sigma) #shape (k,n,n)\n",
    "    \n",
    "    # *********\n",
    "    # compute an (m,k,n,1) array \n",
    "    # such that the i,j-th entry equals x[i]-mu[j] (as a column vector)\n",
    "    x_normed = x.reshape((m,1,n,1)) - mu.reshape((1,k,n,1)) \n",
    "\n",
    "    # and its transpose\n",
    "    # shape (m,k,1,n)\n",
    "    x_normed_T = np.transpose(x_normed, (0,1,3,2)) \n",
    "    # *********\n",
    "\n",
    "    # shape (m,k)\n",
    "    exponents = (x_normed_T @ inv_sigma @ x_normed).reshape((m,k))\n",
    "\n",
    "    # shape (m,k)\n",
    "    joint_unscaled = det_sigma**(-0.5) * np.exp(-0.5* exponents) * phi\n",
    "    joint_unsup = (2*np.pi)**(-n/2) * joint_unscaled\n",
    "    if not with_supervision:\n",
    "        return joint_unsup\n",
    "    \n",
    "    m_tilde = x_tilde.shape[0]\n",
    "    z = z.reshape((m_tilde,)).astype(int)\n",
    "    \n",
    "    #shape (m_tilde,n,1)\n",
    "    mu_z = mu[z].reshape((m_tilde,n,1))\n",
    "    \n",
    "    #shape (m_tilde,n,1)\n",
    "    x_tilde_normed = x_tilde.reshape((m_tilde,n,1)) - mu_z\n",
    "    \n",
    "    # shape(m_tilde, 1,n)\n",
    "    x_tilde_normed_T = np.transpose(x_tilde_normed, (0,2,1))\n",
    "    \n",
    "    # shape (m_tilde,n,n)\n",
    "    inv_sigma_z = inv_sigma[z]\n",
    "    \n",
    "    #shape (m_tilde,)\n",
    "    exponents_tilde = (x_tilde_normed_T @ inv_sigma_z @ x_tilde_normed).reshape((m_tilde,))\n",
    "    \n",
    "    # shape(m_tilde)\n",
    "    p_z = phi[z]\n",
    "    \n",
    "    # shape (m_tilde,)\n",
    "    det_sigma_z = det_sigma[z]\n",
    "    \n",
    "    # shape (m_tilde,)\n",
    "    joint_sup_unscaled = det_sigma_z**(-0.5) * np.exp(-0.5* exponents_tilde) * p_z\n",
    "    joint_sup = (2*np.pi)**(-n/2) * joint_sup_unscaled\n",
    "    \n",
    "    return joint_unsup, joint_sup"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Function to train a classical EM model and plot the log likelihood over time:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def run_em(x, w, phi, mu, sigma):\n",
    "    \"\"\"Problem 3(d): EM Algorithm (unsupervised).\n",
    "\n",
    "    See inline comments for instructions.\n",
    "\n",
    "    Args:\n",
    "        x: Design matrix of shape (m, n).\n",
    "        w: Initial weight matrix of shape (m, k).\n",
    "        phi: Initial mixture prior, of shape (k,).\n",
    "        mu: Initial cluster means, list of k arrays of shape (n,).\n",
    "        sigma: Initial cluster covariances, list of k arrays of shape (n, n).\n",
    "\n",
    "    Returns:\n",
    "        Updated weight matrix of shape (m, k) resulting from EM algorithm.\n",
    "        More specifically, w[i, j] should contain the probability of\n",
    "        example x^(i) belonging to the j-th Gaussian in the mixture.\n",
    "    \"\"\"\n",
    "    # No need to change any of these parameters\n",
    "    eps = 1e-3  # Convergence threshold\n",
    "    max_iter = 1000\n",
    "\n",
    "    # Stop when the absolute change in log-likelihood is < eps\n",
    "    # See below for explanation of the convergence criterion\n",
    "    it = 0\n",
    "    ll = prev_ll = None\n",
    "    \n",
    "    m,n = x.shape\n",
    "    k,= phi.shape \n",
    "    \n",
    "    # initial joint distribution\n",
    "    # shape (m,k)\n",
    "    joint = joint_pdf(x, phi, mu, sigma)   \n",
    "    \n",
    "    ll_hist = []\n",
    "    while it < max_iter and (prev_ll is None or np.abs(ll - prev_ll) >= eps):\n",
    "        pass  # Just a placeholder for the starter code\n",
    "        # *** START CODE HERE\n",
    "        it+=1\n",
    "        # (1) E-step: Update your estimates in w\n",
    "        \n",
    "        # shape (m,k)\n",
    "        w = joint / joint.sum(axis = 1, keepdims=True)        \n",
    "        \n",
    "        \n",
    "        # (2) M-step: Update the model parameters phi, mu, and sigma\n",
    "        \n",
    "        # scaling factor (denominator for mu and sigma, enumerator for phi)\n",
    "        # shape (k,1)\n",
    "        w_column_sums = np.sum(w.T,axis = 1, keepdims=True)\n",
    "        \n",
    "        # shape (k,n)\n",
    "        mu = w.T @ x / w_column_sums\n",
    "        \n",
    "        # shape (m,k,n,1)\n",
    "        x_normed = x.reshape((m,1,n,1)) - mu.reshape((1,k,n,1))\n",
    "        # shape (m,k,1,n)\n",
    "        x_normed_T = np.transpose(x_normed, (0,1,3,2))\n",
    "        \n",
    "        # shape (k,n,n)\n",
    "        sigma_unscaled = np.sum(w.reshape((m,k,1,1)) * x_normed @ x_normed_T, axis=0)\n",
    "        sigma = sigma_unscaled / w_column_sums[...,np.newaxis]\n",
    "        \n",
    "        #  shape (k,)\n",
    "        phi = w_column_sums.reshape((k,)) /m\n",
    "        \n",
    "        # (3) Compute the log-likelihood of the data to check for convergence.\n",
    "        # By log-likelihood, we mean `ll = sum_x[log(sum_z[p(x|z) * p(z)])]`.\n",
    "        # We define convergence by the first iteration where abs(ll - prev_ll) < eps.\n",
    "        # Hint: For debugging, recall part (a). We showed that ll should be monotonically increasing.\n",
    "        prev_ll = ll\n",
    "        \n",
    "        # shape (m,k)\n",
    "        joint = joint_pdf(x, phi, mu, sigma)\n",
    "        \n",
    "        # sum_z[p(x|z) * p(z)]\n",
    "        # shape (m,)\n",
    "        margin= np.sum(joint, axis=1)\n",
    "        \n",
    "        ll = np.sum(np.log(margin))\n",
    "        ll_hist.append(ll)\n",
    "        # *** END CODE HERE ***\n",
    "    print(\"Converged after {} iterations\".format(it))\n",
    "    plt.figure()\n",
    "    plt.title('Log-Likelihood')\n",
    "    plt.xlabel('Iteration')\n",
    "    plt.ylabel('L_unsup')\n",
    "    plt.plot(ll_hist)\n",
    "    return w"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Helper function to plot predictions (I changed it to not save the plots):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_gmm_preds(x, z, with_supervision, plot_id):\n",
    "    \"\"\"Plot GMM predictions on a 2D dataset `x` with labels `z`.\n",
    "\n",
    "    Write to the output directory, including `plot_id`\n",
    "    in the name, and appending 'ss' if the GMM had supervision.\n",
    "\n",
    "    NOTE: You do not need to edit this function.\n",
    "    \"\"\"\n",
    "    plt.figure(figsize=(12, 8))\n",
    "    plt.title('{} GMM Predictions'.format('Semi-supervised' if with_supervision else 'Unsupervised'))\n",
    "    plt.xlabel('x_1')\n",
    "    plt.ylabel('x_2')\n",
    "\n",
    "    for x_1, x_2, z_ in zip(x[:, 0], x[:, 1], z):\n",
    "        color = 'gray' if z_ < 0 else PLOT_COLORS[int(z_)]\n",
    "        alpha = 0.25 if z_ < 0 else 0.75\n",
    "        plt.scatter(x_1, x_2, marker='.', c=color, alpha=alpha)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Helper function to load data (no changes made):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def load_gmm_dataset(csv_path):\n",
    "    \"\"\"Load dataset for Gaussian Mixture Model (problem 3).\n",
    "\n",
    "    Args:\n",
    "         csv_path: Path to CSV file containing dataset.\n",
    "\n",
    "    Returns:\n",
    "        x: NumPy array shape (m, n)\n",
    "        z: NumPy array shape (m, 1)\n",
    "\n",
    "    NOTE: You do not need to edit this function.\n",
    "    \"\"\"\n",
    "\n",
    "    # Load headers\n",
    "    with open(csv_path, 'r') as csv_fh:\n",
    "        headers = csv_fh.readline().strip().split(',')\n",
    "\n",
    "    # Load features and labels\n",
    "    x_cols = [i for i in range(len(headers)) if headers[i].startswith('x')]\n",
    "    z_cols = [i for i in range(len(headers)) if headers[i] == 'z']\n",
    "\n",
    "    x = np.loadtxt(csv_path, delimiter=',', skiprows=1, usecols=x_cols, dtype=float)\n",
    "    z = np.loadtxt(csv_path, delimiter=',', skiprows=1, usecols=z_cols, dtype=float)\n",
    "\n",
    "    if z.ndim == 1:\n",
    "        z = np.expand_dims(z, axis=-1)\n",
    "\n",
    "    return x, z"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Train models and plot their Log-Likelihood and their predictions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Running unsupervised EM algorithm...\n",
      "Converged after 164 iterations\n",
      "Running unsupervised EM algorithm...\n",
      "Converged after 168 iterations\n",
      "Running unsupervised EM algorithm...\n",
      "Converged after 119 iterations\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(229)\n",
    "# Run NUM_TRIALS trials to see how different initializations\n",
    "# affect the final predictions with and without supervision\n",
    "for t in range(NUM_TRIALS):\n",
    "    main(is_semi_supervised=False, trial_num=t)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Semi-supervised EM Implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def run_semi_supervised_em(x, x_tilde, z, w, phi, mu, sigma):\n",
    "    \"\"\"Problem 3(e): Semi-Supervised EM Algorithm.\n",
    "\n",
    "    See inline comments for instructions.\n",
    "\n",
    "    Args:\n",
    "        x: Design matrix of unlabeled examples of shape (m, n).\n",
    "        x_tilde: Design matrix of labeled examples of shape (m_tilde, n).\n",
    "        z: Array of labels of shape (m_tilde, 1).\n",
    "        w: Initial weight matrix of shape (m, k).\n",
    "        phi: Initial mixture prior, of shape (k,).\n",
    "        mu: Initial cluster means, list of k arrays of shape (n,).\n",
    "        sigma: Initial cluster covariances, list of k arrays of shape (n, n).\n",
    "\n",
    "    Returns:\n",
    "        Updated weight matrix of shape (m, k) resulting from semi-supervised EM algorithm.\n",
    "        More specifically, w[i, j] should contain the probability of\n",
    "        example x^(i) belonging to the j-th Gaussian in the mixture.\n",
    "    \"\"\"\n",
    "    # No need to change any of these parameters\n",
    "    alpha = 20.  # Weight for the labeled examples\n",
    "    eps = 1e-3   # Convergence threshold\n",
    "    max_iter = 1000\n",
    "\n",
    "    # Stop when the absolute change in log-likelihood is < eps\n",
    "    # See below for explanation of the convergence criterion\n",
    "    it = 0\n",
    "    ll = prev_ll = None\n",
    "    ll_hist =[]\n",
    "    m,n = x.shape\n",
    "    k,= phi.shape \n",
    "    m_tilde,_ = x_tilde.shape\n",
    "    \n",
    "    # initial joint distribution\n",
    "    # shape (m,k)\n",
    "    joint_unsup = joint_pdf(x, phi, mu, sigma)\n",
    "    \n",
    "    while it < max_iter and (prev_ll is None or np.abs(ll - prev_ll) >= eps):\n",
    "        pass  # Just a placeholder for the starter code\n",
    "        # *** START CODE HERE ***\n",
    "        it+=1\n",
    "        # (1) E-step: Update your estimates in w\n",
    "        \n",
    "        # shape (m,k)\n",
    "        w = joint_unsup / joint_unsup.sum(axis = 1, keepdims=True)\n",
    "        \n",
    "        # (2) M-step: Update the model parameters phi, mu, and sigma\n",
    "        \n",
    "        # w_tilde[i,j] = 1{z[i]==j}\n",
    "        # shape (m_tilde,k)\n",
    "        w_tilde = z == np.array(range(k))\n",
    "        \n",
    "        # scaling factor (denominator for mu and sigma, enumerator for phi)\n",
    "        # shape (k)\n",
    "        w_column_sums = np.sum(w,axis = 0)\n",
    "        # shape (k,)\n",
    "        w_tilde_column_sums = np.sum(w_tilde, axis=0)\n",
    "        # shape(k,)\n",
    "        weighted_sum = w_column_sums + alpha* w_tilde_column_sums\n",
    "        \n",
    "        # shape (k,n)\n",
    "        mu_enumerator = w.T @ x + alpha* w_tilde.T @ x_tilde\n",
    "        mu = mu_enumerator / weighted_sum.reshape((k,1))\n",
    "        \n",
    "        # shape (m,k,n,1)\n",
    "        x_normed = x.reshape((m,1,n,1)) - mu.reshape((1,k,n,1))\n",
    "        # shape (m,k,1,n)\n",
    "        x_normed_T = np.transpose(x_normed, (0,1,3,2))\n",
    "        \n",
    "        # shape (m_tilde,k,n,1)\n",
    "        x_tilde_normed = x_tilde.reshape((m_tilde,1,n,1)) - mu.reshape((1,k,n,1))\n",
    "        # shape (m_tilde,k,1,n)\n",
    "        x_tilde_normed_T = np.transpose(x_tilde_normed, (0,1,3,2))\n",
    "        \n",
    "        # shape (k,n,n)\n",
    "        sigma_enum_sup = np.sum(w.reshape((m,k,1,1)) * x_normed @ x_normed_T, axis=0)\n",
    "        sigma_enum_unsup = np.sum(w_tilde.reshape((m_tilde,k,1,1)) * x_tilde_normed @ x_tilde_normed_T, axis=0)\n",
    "        sigma_enum = sigma_enum_sup + alpha* sigma_enum_unsup\n",
    "        sigma = sigma_enum / weighted_sum.reshape((k,1,1))\n",
    "\n",
    "        \n",
    "        #  shape (k,)\n",
    "        phi = weighted_sum/(m+alpha*m_tilde)\n",
    "        \n",
    "        # (3) Compute the log-likelihood of the data to check for convergence.\n",
    "        # Hint: Make sure to include alpha in your calculation of ll.\n",
    "        # Hint: For debugging, recall part (a). We showed that ll should be monotonically increasing.\n",
    "        prev_ll = ll\n",
    "        \n",
    "        # shape (m,k) , (m_tilde,)\n",
    "        joint_unsup, joint_sup = joint_pdf(x, phi, mu, sigma, with_supervision=True, x_tilde=x_tilde, z=z)\n",
    "        \n",
    "        # sum_z[p(x|z) * p(z)]\n",
    "        # shape (m,)\n",
    "        margin= np.sum(joint_unsup, axis=1)        \n",
    "        ll_unsup = np.sum(np.log(margin))\n",
    "        \n",
    "        ll_sup = np.sum(np.log(joint_sup))\n",
    "        ll = ll_unsup + alpha* ll_sup\n",
    "        ll_hist.append(ll)\n",
    "        \n",
    "        # *** END CODE HERE ***\n",
    "    \n",
    "    print(\"Converged after {} iterations\".format(it))\n",
    "    plt.figure()\n",
    "    plt.title('Log-Likelihood')\n",
    "    plt.xlabel('Iteration')\n",
    "    plt.ylabel('L_semi-sup')\n",
    "    plt.plot(ll_hist)\n",
    "    return w\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Train models and plot their Log-Likelihood over time and their final class assignments:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Running semi-supervised EM algorithm...\n",
      "Converged after 19 iterations\n",
      "Running semi-supervised EM algorithm...\n",
      "Converged after 21 iterations\n",
      "Running semi-supervised EM algorithm...\n",
      "Converged after 23 iterations\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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keyIiIqIy87uF4w4A/5dS6iSAJwDcpZT6u8wLaa0f01pv0FpvWLZsWaXHSKZa3CWV56lzQF2jfE9ERERUZr62cGit/xDAHwKAUuodAO7XWv+2n2OiAOkIS9vGaETCM9s3iIiIqAJM6IEmKl5HmMGZiIiIKsqYAK21/h6A7/k8DCIiIiKivPzugSYiIiIiChQGaCIiIiIiFxigiYiotnFBJiJyyZgeaCIioorjgkxEVARWoImIqHZxQSYiKgIDNBER1S4uyERERWALBxER1S4uyERERWCAJiKi2sYFmYjIJbZwEBERERG5wABNREREROQCAzQRERERkQsM0ERERERELjBAExGRGbgiIBEFBGfhICIi/3FFQCIKEFagiYjIf1wRkIgChAGaiIj8xxUBiShA2MJBRET+44qARBQgDNBERGQGrghIRAHBFg4iIiIiIhcYoImIiIiIXGCAJiIiIiJygQGaiIiIiMgFBmgiIiIiIhcYoImIiIiIXGCAJiIiIiJygQGaiIiIiMgFBmgiIiIiIhcYoImIiIiIXGCAJiIiomAZiwIn+uQrkQ9Cfg+AiIiIyLGxKDC4FZiNA3VNwNv7gI6w36OiGsMKNBEREQXHaETCc/MKYDYh3xNVGAM0ERH5j4fkyanFXVJ5njoH1DXK90QVxhYOIiLyFw/JkxsdYXmNjEYkPPO1Qj5ggCYiqlVjUTNCiP2Q/NQ5+Z6hiPLpCPM1Qr5igCYiqkUmVX15SJ6IAoYBmoioFplU9eUheSIKGAZoIqJaZFrVl4fkiShAGKCJiGoRq75EREVjgCYiqlWs+hIRFYXzQBMRUXBwvmgiMgAr0EREFAwmzRxCRDWNFWgiIgoGLuFMRIZggCYiomAwbeYQIqpZbOEgIqJg4MwhRGQIBmgiIgoOzhxCRAZgCwcRERERkQsM0ERERERELjBAExHVCs6hTETkCfZAExHVAs6hTETkGVagqwUrS0SUj5s5lMv1fsL3KSKqEqxAVwNWloioEKdzKJfr/cR+u1oDN28DVnfzvSpoxqKcRpAIDNDVwV5Zmjon3/ONjYjsnM6hXK73E+t2Q23A2GHg6G7glX7u8AcJizVEaWzhqAZcnYuInOgIAzdtzR96yvV+Yt3u5LB839LJ5biDhkupE6WxAl0NuDoXEXmlXO8n1u0ODwDHe4FkjDv8QcNiDVGa0lr7PQZXNmzYoJ9//nm/h0FERMViH21w8bmjGqKUOqS13pDtd75WoJVSzQB+AKApNZava613+TkmIiIqMy7HHVx87ogA+N8DHQdwl9b6ZwF0AXiXUurnfB4TERERBU0tTpNYi4/ZEL5WoLX0j8RS3zak/gWrp4SIisNDwcXhdiNaqBZnCKnFx2wQ308iVErVAzgEYB2APVrr57Jc5l4A9wLAjTfeWNkBEpH3+MZfHG43KlW17oDV4nSutfiYDeJ3Cwe01jNa6y4AnQDeqpR6Y5bLPKa13qC13rBs2bLKD5KIvMXpsIrD7UalsHbAon8iX6vpsH8tzhBSi4/ZIL5XoC1a6zGl1PcAvAvASz4Ph4jKiW/8xeF2o1JUc8WyFqdzrcXHbBC/Z+FYBmA6FZ5bAPwygAf9HBMRVQDf+IvD7UalqPYdsFqcIaQWH7Mh/K5ArwTwN6k+6DoAX9NaD/g8JiKqBL7xF8fNdgtav2vQxhs03AEj8ozfs3AcBvBmP8dARFSVgnbCYdDGG1TccSXyhO8nERIRURkE7YTDoI2XiGoaAzQRUTUKWr9r0MZLRDXN7x5oIiL/VHPPbdD6XYM2XiKqaQzQRCar5oDnNxN6bsv9/Aat3zVo482Hf7tEVY0BmshUJgS8aub3nLh8fqsXn1tzcceGPMIeaCJT8aSq8vK755bPb/Xic2umal6JkSqOFWgiU/kd8Kqd3z23fH6rF59bM/l91ImqCgM0kan8Dni1wM+e23I8vzw8bQY+t2bijg15SGmt/R6DKxs2bNDPP/+838MgIjIL+26rF59b73BHhFxQSh3SWm/I9jv2QBMRVdpYFDjR520PJvtuqxefW+90hIGbtjI8U8nYwkFEVEnlqiby8HT14nNLZBwGaCKiSso8kWl4wJtDyuyZr158bomMwwBNRFRJ9mqingWO9wJKeVONrqaFSGg+PrdERmEPNBFRJVnVxPAfATdvk/DM3lYiokBhgCYiqjTrRKbV3extJfOU4yRXoirDFg4iIr+wt5VMwynziBxhgCYi8hN7W2uL6fMQc7U+IkcYoInIHKaHC6JSBKG6yynziBxhgCYiMwQhXAAM+UFkynMWhOou24qIHGGAJiIzBCFcBCXk0xyTnrOgVHe9aCsyZaeFqEwYoInIH5kfsEEIF0EI+TSfSc9ZrVR3TdppISoTBmgiqrxcH7Cmh4sghHyaz7TnrBZOGjVpp4WoTBigiajycn3Amh4ughDyaT4+Z5Vn2k4LURkwQBNR5QX5A9b0kE8L8TmrLO60UA1ggCYi7zg9cYgfsGQinvjmHe60UJVjgCYib7g9cYgfsGYHNpPHVg488Y2IXGCAJiJv8MQhd0wObCaPrVxMe/3W2g4MUcDU+T0AIqoSQe5r9oM9sM0m5HtTmDy2QsaiwIk++ermcia9fq0dmOifyNdCj4WIKo4VaCLyBvua3fEqsJWjUmlSmHTDaeXc9GkUTauGE9ECDNBE5B32NTvnRWArV6uFSWHSDafB0/RpFIO0A8NWE6pRDNBERH4pNbCVs1JpSph0w2nwLHQ5v0NhUHZgarFXniiFAZqIKKiCVKmsBKfBM9/lTAmFQdiBYasJ1TAGaCKioCq2Uul3hbWcnAbPXJfzMhSWup1Nf5783IEzfdtQ1WOAJiIKMreVSlMqrKby8uTOUrazl89TucKmX60mfA2TARigiSg/Vnqqi5+H3cv1WnJ7u2NRYHhA/r+6e/51vAqFpW5nr56ncodNP1pN2DpCBmCAJqLcWOmpPn4ddi/Xa8nt7Y5FgWc3A1dOyvfHe4E79y4M0aWOrdTt7NXzVI1hk73/87HI4QsGaCLKrRo/fGudX4fdy/Vacnu7oxEgOQ6gHlAApifK87r2Yjuv2SJfM6vkblRr2PRi21QDFjl8wwBNRLlV64dvrfPjsLub15Kbipp1u1dOAToJhFrz3+7kaUArQCfka0Nb+V7XxW7nzFC0uru0MQRhSjynvNw21YBFDt8wQBNRbtX24Uv+cfpacltR6wgDb+oBDu0AVAj48S6gbd3C61i3Oz0OJC4CoTagvgnoetC817XXoSgIU+I5ZdIsKSZgkcM3DNBElJ/9w9f+gQME/8OHKstJkCsmICVjQOia/Nexbre+GdAAWlbMXdc0DEW5mTJLiilY5PANAzQROWP/wNFafqZU+T58qqE6RO4VE5CcXMe6zPQEoOqAmXh52zeycfqaZijKzZRZUkxSTUcYAoQBmoicsX/gTByVEN1+S3k+fKqlOkTuFROQnFzHfplQq1SeTZ67uFZCUTE7yibMkkI1jwGaiJyxf+CE2uRn5frwqabqELlXTEBych0/Qylf0wv5uaPMKj+ViAGaiJzJ/MAByvfhw+oQVRu+phfye6eiVqr8VBYM0ETkXOYHTrk+fCpRHWKPtXmq+TlhxXMh7lRQgDFAE5GZylkdKnTo2Msgl+22ghoUyznuShzO93u7V7ri6ffjLYQ7FRRgDNBEVHvyHTr2Mshluy3Am9uvdDgqd8At9+H8Wjsx1avHW+7XGdsoKKDq/B4AEVHF5Tt0bA9yswn5vpCxKHCiT77aZbutYm4/2/0NbgWifyJfM++3HDLHPTyQ/TEXq9yH873Y7n7K9RrLJaivM6KAYAWaiArz+1Cw1/ef79Cx2yCXr9KX67ZKDYp+nHxlfyx6Fjje6+084OU+nB/kfttiqslePF6/T/Lzgt/vXVS1GKCJKD+/D32X6/5zHTp2G+TyhYxct1VqUPQjDNofy+Rp4MTj3gerch7OLzWgFwpi5QxqxQRZL3ZIgrzTAfj/3kVVjQGaiPLzuwrlx/27CXKFQka22yo1KPp18pU17rEo8Ep/8IJVsdvdyUmn5QxqxQbZoL7OvOL3exdVNQZoIsrP7yqU3/dfiN9h1g9BD1ZuFQpi5Q5qfm7vIJ/k5/S9g20eVAQGaKKg8OtN3u+w5Pf9OxGkkOHV6yhIj7lUhYJYJXbyaml7e8XJewfbPKhIDNBEQeD3m7zfH95+33+18Pt1FFSFglgQdvJqVaH3DrZ5UJF8ncZOKXWDUupflFJHlFJRpdTv+zkeImMFfQquSnM75VetKPQ6qobtVq7H0BEGbtqaO1wV+n05Bfl583vspreIkbH8rkAnAXxUa/0fSqk2AIeUUt/VWv9vn8dFZBa+yTvntspaS/2P+V5H1VCdrobH4FaQH7MJY+fRAyqSrwFaa30WwNnU/yeUUkcArAbAAE1k5/ZNvpZCYSY3h2RN+ACvpHyvo2o4lF2px2DS31cpj9nvx+F27OUaL1vEqAh+V6DTlFJrAbwZwHP+joTIUE7f5IMSCsv1YeimWl8NodGtXK+jIB3lyPXaqcRjyPf35UcgLfYxm/A+4WbsJow325hM2ZGiijMiQCulWgHsBfARrfV4lt/fC+BeALjxxhsrPDqigAlCKCznh6Gban2QQmO5lXIou5JBwnrtTI8DM1eBNVuA190zt2NQ7sPxuf6+/Ap4xT5mE94n3IzdhPHamRjoqaJ8D9BKqQZIeO7TWn8j22W01o8BeAwANmzYoCs4PKLgCUIorMS8uU5uj/2P8xVzKLvSQWI0IuF56jUJ0EcfAc7sA+7cOzf+ct5/rr+vSga8zB2WYh6zKe8TTsduyngtpgV6qjhfA7RSSgH4MoAjWusv+jkWoqoRhFBo2ochLeS0qlzpILG4C9BJmUUEClAhYHqicgEm199XpV7Txe6wZAvdpr9P2Jk2Xr6H1Ty/K9B3APgAgB8rpaz5lD6htd7n45iIgs/0k2JM+TCspsOwXrZRuNkulQ4SHWHg9keAH30YiF8EoIGGtsoGmGx/X9ZrenigvPddzA5LrufTi/eJSrbvmPS+Zsp7GPnG71k4/hWA8nMMROQTEz4Mq+UwrNc7Am62S7mCRL5gdsMmoG3dXFhd3W3O8/ZKv2y7V/rLs0NWzA5LuV7n1bQDWgwn72E80bBq+V2BJqKgqMYPgnJXTyu1zbwOSG63i9c7Q06CmQk7YJm8eB4KvWaK2WEp1+u8WnZAy6XWdzCqHAM0ERVWrR8E5TwMW8lt5nVA8vvwdFCD2eIuQGtg4igQKqKtxOlrxu3OQ7mez3LugFbDDntQX8fkCAM0ERVWzR8E5apkVnKblSMg+VnhDfoJWrrIyaLK+Zopx/NZzvYda0dCa+DmbWa16TgV9Ncx5cUATUSF8YPAPT9OrgtawMjF7wp4sUYjgFJA+y3OVsEsx0wela7cluN1Z+1IhNqAscPAT3aXr6e8nIp9HVdD9b0GMEATUWFBDTR+CuI2M+mDO4g7BE4DcL5ZMUp5zVRLq5W1Ha8Oy/eLOoFkLJhHvty+jqvlOawBDNBE5EwQAw05xw/u0jkNwPlaNUr5O6uWViv7lIDHeyU8u12m3MQZWpyoluewBjBAExGVQ9ACKT+4vWFts9HI/O/tnFSqizka4GXbkN9HI6wdidXd7sYxFgWe3QxcOSnfH++dW6UyCNguFxgM0LXO7zdJomplUiB18nfOD+7SWZXP473SC51vCr58lepid768ahsyaefPbUV+NAIkxwHUyyoTlVyl0gtBbP2qUQzQtcykN0mqfn7urPlx36YEUjdTo/GDu3jWdo6fB+IjQMdt+ft28wXDUna+vGi1Mmnnz63FXUCoXZ4DjcqvUukFtssFAgN0LQvymyQFi587a5W678yQbkogdfp3zqNRpbG2c0unhLfJYaB5WXHhze+dL7/vvxQdYWnZCGoPNAUGA3QtC/KbJAWLnztrlbjvfLMq+P3h7bTftlw7GbUSzK3tnIwB16wtbe5iv3e+/L7/Upnwd0dVjwG6lgX9TZKCw8+dtUrcdyWWcC6Wk7/zcu1k1FKbmNfvp36HQL/vn8hwDNC1jm+SVAl+7qx5eWJVrtsoNaSXO2gWmhki3/hLCfb5gnk1Vqb5fvoTIUQAACAASURBVEpUMwoGaKVUO4BlWuufZvz8Nq314bKNjIiqi1/hwougVijglhrSvexTznaZYsdfarDPFcxrqTJN5VONO2E0n8HPcd4ArZR6L4A/B3BeKdUA4INa6x+lfv04gP+jvMMjoqrhxxthtqAGuB+Hk4Bbyg6CV33KuS5TbItGqa0duYI5T2CmUr36JHBoB6BCQEM7d8KqkeE72oUq0J8AcLvW+qxS6q0AvqqU+oTW+huQGRaJiArz640wM6gNDwCv9LsfR7n7qL3qU851mULjz/X8ePG4s+1YeL09vdw5M7jiRSljUeDQTuDqa0B9IwDFnbBqZPiOdqEAXa+1PgsAWusfKqV+CcCAUqoTMsMiEVFhfr0RZgY1oLhxVKKHu1AF20nozHWZQuPP9fwU87idBFAvt6eXO2eGV7wY7lNGI4Cql9f4zDSgpzmLVDUyfKawQgF6Qin1Oqv/OVWJfgeAbwGo4b9eInLFrzfCzKAGSAW6mHEUCrjlDjdOQme+y+Qbf77nx01ripsA6lVPvJc7ZyZXvIoN99UYuhd3SdsGFKCTwO0PV/fJqbXK8JnCCgXoDyOjVUNrPaGUeheA95ZtVERUHewfZn7OwmG/v3KMo1KVSyehs5hg6tUHlR8B1Muds0rs6BUb8IrZtqZX1B2KRoFIBOjqAsJhlO+kVzKPwTPb5A3QWusXc/x8GkCf9b1S6t+01j/v8diIKMiyfZjdtNXvUZXnDdnkyqVTXmwXPwKol20mpexIOJ0hpdiAV8y2LfS6rES1tsT7iEaBrVuBeBxoagL6+mwh2mkrElEZeDUPdLNHt0NE1aKWPswM79WrmHIfci12xUd7iAMKT+kH5J4z2824MpXyN+Fm21qPN9Saf37vZzcDyXEg1C7LX3v4fEWjwIlIFO9s2YqWxuIrwpEIMD4ONDcDExPyfTjXTZTyd8jWD3LJqwDNEwqpfPjGFkymhspyvJ4M79WrqHIecvWijWHNlsJVWbdVYqfjKvVvwsm2zRz/m3pkefHM1+XwAHDlJIB6ID4i33v0vFlV4195fQRvuDOO5WtW4BoUtxPd2gqcPQvMzgJ1dfL9gpYOS7F/h2z9oCJwJUIyG9/YgsvEUFnO15PBvXqe82un1os2BiD/bRQT0p2Oy+3fRDHbOXP8yVj+1ikFT0tg0SiwZ49UjS/OdCGRbMJ07BywuLid6FgMWLlSKtDxODA0BOzalaWlw1LE32H0uROIPPMr6Fp/EeEVz1X30TLyjKMArZR6g9b6f2f87B1a6+9Z33o9MCIAtdUGUI1MC5VBfT2ZdBTGz53aYnbKMsPt6m755+Wy7G7G5fRvotjt7HT8q7uB473A9ATQ0CbfO5SrAmxVnsfHpWr8AxXG+OU+7O6JoOONxb12u7qA9nYgkQDa2uRn8TiwYgVw7lyBlg6Hj2XrR9+J+OU3oCmUQN/H/wjhXzDkaBkZzWkF+mtKqa8C+Byk3/lzADYAsE4c/EAZxkZkbhsABVMQX0+mHYXxeyfE7U5ZrnCbb3q9Yo6cWOMaiwIn+krf2Sl2Ozsdf0dY+p6HB1wNK+dJfZAwG48Da9YASgEbNwLbt4fRmSfh5mzHsP2up0cq0V2pP9f+fgnPjY1zPytWJALEZ1qwYu1ynDs7jUj9boQ7Oku7UaoJTgP02wA8CGAQQBtkBo47rF9qrV/yfmhEMLMNgIIriK8nvwNrJhN3QgpV6N2eGFjskRMvd3ZK2c5uxm+tzPlKv6PxWiF5xQrg1Clp19i+XcJvV5eE6nPnpFq8caNc/tixuQCcrWKdLYzn+11fX+7Q7VZ6zJeuQWMr0HVHR2k3SDXDaYCeBnAVQAukAn1Caz1btlER2ZnWBkDBFrTXU7FBKl+oLKUlxLSdECehtVJVfC93diqxnYsYrxU4T50CzpwBnnoK+Pa3gfvvB667bq5a3NoqvcpWO8fKldKKka1ina0dI9/vwuHSg7MlHPY2kFPtcBqgfwTgSQBvAbAEwF8qpd6jtX5P2UZGRETFz3OcKzB6ESZN2glxEgIrVcX3ujpf7u1cxHitwLlnj4TnsTHpT/7oR4HOTmmr2LZNLhuPSyvH9LR8TSTmB2F7xTqzHSPf74hM4DRA36O1fj71/9cAbFJKse+ZiMxk0kl3XnAbpPIFRj9aQspVDQechcBKtZ2YWJ0vdun3PMJhadv49rclHNfVyTRzSgEnTwK7d0u1OR4HTp8GZmbk5zfeOD8I56v+Oq0M5+uhtn4/kGrz7u7O3medq1WEKB9HAdoWnu0/+6r3wyEiKpFpJ935IV9grHQPcyWq4VYIDLVm73OuZLDN3Nnxa2fO6bYtssodDgMPPwzs2AFoDVy8KAudAFKJjsWA9euBV1+Vn83OSrXaCrPh8MLwa/8ecBae84XfaBTYvFnCOwD09gJ7986/TL5WEaJ8OA80EVUX006680O+wFiJuYjtKlENt65TaIXBSgfY4QGZKk6pyu/MlfHvwB50n35a/t/aKnM09/ZKeG5sBG69Ffjnf5aHr7X0Q3/hC3KZd78b2LdPftfUJL3T1vzOOjUvtXW9bduyV48LhV9rFcP6evk+20qGbBWhYjFAE1F1MXGWCD/kC4zlnovYrlLVcJN2nKztFj8vq/x13CYLmpRrTNl2csr0d5Ct6rs1tU7Lpk0SdO1V5G9+U6rQMzNShZ6YkEp0by9w9Spw220SuA8cmAvDR49KcO7sBA4flpaQ/v6FFeZC4deaQ3pkRL5va5Og39c3V9nmSYRULAZoIq9UW99tUJnWhxpkXoRSL6vh+Zi042Rtt5ZOCdCTw0DzsrkxWdVpQBYwKeVx59rJKbBtC/UO2y83MCAhdfly+Vm+qm/mDBkDA8CnPz0XkKen5edLl0prxcmTwKpVMuXdM89IeG5slGA8PCyXtVpCrPuyjz1f+A2HpWXDGj8APPDAXNXbCuRezupBtYMBmsgL7Ls1i5MKK3d4srNvF69CqRfVcCf3YcqOk7XdkjHgmrXAzdvmgvJYFHh2M3DlpFz2eK8saFLsePPt5OTYtk5PnLN6iI8fB5JJIBQCVq921/IQDgOf/KS0d0xMSNVZKalKKyXtFT09wLp1cvnpaalU//f/DkxOzm8J6erKXwHPHLsVrLu75TLnz0s12qp6s9+ZSsEATbWjnIHJpMPHVBh3eLLLtl1MCaVOmDK9Xr4wPxoBpscBlWrMTU6U9n5RxE6O1Tvc1iZV3oGB7EHS6iFWSr63pqK77z6pCjttechskxgYkLaMzk7g0iWpTg8NyW3HYvL1s5+V/ml7S4h1O4VO+ssM2Vu2yP87OyVADw8Dy5ax35lKwwBNtaHcgcmkw8e1pNidIu7wZJdtu9y0tfhV+aznxrrtIIRwr+QK84u7gIZ2IJFqzA21lfZ+UUTlvatLeowPH5bve3uzn6Rn9RBfvCiXn5mRSnCu6eDytYRktkn090t4PnMG2L9fbtdeob50SYL2Aw/k73vO7GkGFp5cCMh1YjFg7drcJyUSucEATbWh3IHJpMPHtaKUnaJq3eGpxJzKTsdhPTf2KRVY7ZfHfude73qgrdt0cRvhsIRIqwqcr51h2zYJx08/Pdc7nMntXMr2xVj27wfWrJGVDVetAkZHgYYGCesvvCC3ndn33NMjVetbb52bucN+v5khu7t7YSXbN2wdqxoM0FQbKhGYTDl8XCtK2Smqxh0er+dULmW72J+bidSUCu23sNpvKdN7hdMTAwEJlP398/uLM2/LCsVXrki7x5o1uaeLs1pCTp6UkwY/+cnCIXr7dmBwcG5Z8CVLpCd60SIZ1w9/KGPINcXdwID0ZWeOK9/MGpHI3P1XHFvHqgoDNNWGagxMta7UnaJiQ4ypFSQv51Qu9XFZz82VU5J48j1PTrenqds9k0/jdLKoiD1QFpq+bWBATrrr7JSe5GQy+4mD0aisNjg1Bfz0p3K5b3xDbjdz0ZJM2SrRTU3ATTfJiYtWMM42xd0ttwDHjkmP9qlTEt4zVznMfPy+rzjI1rGqwgBNtYMV4urix06RyRUkE9pS7OHxTT3AoR1AfbOM56a7F7YrON2eld7uxYZgH18f+RYVyRUec03fFo1KX/TIiPxbuxb44helKmwP2/bbnZqS1gtAqsgTExLCc600aN3GsWNyH1rLuBsaZJaM06clGE9PS6vG4OBcgJ+akutdvChV6+lpqVLnC8RGrDhowt8oeYYBmoiCq9I7RSZXkPw+ypIZHtdsAULXzG2rRZ0Lx+R0e1Zyu5cSgn18feRbVMRteIxEpEXitttkxopt22SRlGyXs253dFROANRaAu30tITwbCsNWiH+2DHg/e+XfmelgPe9T9o2nn56LpS3tABf/rJc//vfl7YTa1nw9nbg9a+XxxSLOds+p05Jlby1tbjtXBK//0bJU3V+D4CIKDAyK0ihVuBEn4QuE3SEi581w6mxaPbHbA+Pswn5WaFqm9OKXCUrd5mPYzTi/Lo+Vhitdog/+iP3K/Zlsi4fi8l0b+vXy21Gowsvp7X8/MKFuf5kQMJvIiHhOpGY34aRSEj4PnBAwmxDg1z3zBkJ0tZllJI2jkRCprnbu1eqzhcvyu2PjkogdjofdU+PBPv6egnzmY+nIirxN0oVwQo0EZFT9gpSqBX48S4z2zmcctuqkK86mxkeV3fLv3y377Qi53XlLt/jLiUE+1xhzNWS4Xa5avvlW1slbI6PS6X44YcXVqOvXpWqsJ01k4YV2u0rDVr9yiMjcpnJSbnOTTdJOD6Vap1Xau7ygATf+vq50L1smdzu9u3O2jFiMeCaa3xu46CqwQBNRNWjEidwWW0jJ/rMbedwophWhUKr3mULj4Vu02kbjlftOoUed6kh2O04y/SazXbSoJuwaD/RcHxcTiicngZ27JCAe/AgcPmyVIevv35+C0VdnYTbBx+Un4+MSOvFxIQE43h8bnnttjaZ5UMpqUh/7GOyiMrkpFy3uVkC+Pr10rIxPS3XW7ZM+p+dhmfrZEer1zrXzCNGTHVHgcAATUTVwYsTuNyEmaCfEFRMv26hx+zHibpuA6iTx13q48g2plw/K8NJh17OONHVJVXi6Wmp+iYSssx2Mim/b2gAli+XQHrNNVIh/sAHgHvukft88kngv/wXuf7MjFx2eBj4whckgM/MyL/mZmnL2LdPFlGZnpbbn5yUyw8Nza+KDw3J748dKxx67dsDAO6+e+FCKkbM0uGXoMxwYxgGaCKqDqWewOU2zAT9hKBidgBMe8zFBNDFqcbdiaOlrwLodExA9nGW6aTDYmecyFaBDYeB++8HPvUpmZ95clLaNerqZDO2tAC/8RvSSmGF2u5u+drXB/zTP80F5CtXpJINzC3IsnIlcPasBObxceBHP5LL21mLqnR3S8iNRufaSs6eldtob88dejO3R2fnwssZMUuHH0yeWchwDNBEVB1KrQgXE2aCPDVisWHYpMec7Tmzfl7oMdnPeMtUSkUu15iyvbbKdBTD7UmDgFSKd+6UCrI9jD75JPDQQxKUlQI+9CGpHlsn+V13nbRRALLs9vi49EnPzsp1rF5mq/p7/fXS0hGPSwhvbJR2jJkZmS7v0iW57YmJ+eOzFlWxqtDxuITy2Vn5ap2YmC30Zlv++8EH5XdWJbqYbZZPYNpBTJ5ZyHAM0ERUHUqtjga9JaMYJoXhYmSbFSVfNW0sChzdI7Nr5FoZsdSKXK7XUbaflami7/SkQSvktbZKb/Nrr0l4VEp+/swzwB/+4Vxbw/LlwLXXSmA+ckTmZ7ZaNR58UFYhVEpaMerqJEAvXy6XP3MGeO45+VlHh0yNt3699Dm3tkr4Hh6WnujPfEZmzBgdTW26OmDpUgnXe/ZItbupaS5kX7woQT5X6M08KfKBB2SsgEy1Zy344uZEy3w8aQepVFtFLb7veYQBmoiqRymB0LT2BCos8znLV02zgvH0OHD1LAAFNGRp4Si1IpfrdZTrtVWmnRjrJMBoVAJcZii0hzyrLaOxUVopkkmpEn/0o3O9yIBc7tFH5Trt7cDnP78wGFqzcdTXz80HbYVse1UWmP9/QKrI4+PAjTfKyYS7d8uJgi+/LIF3YkJWLBwclIA9NDQ3nnhc5osGJLRbbSTZVl8cH5fxAXKb9iXAvagWl9wOUsm2Cr7vFY0BmoiqUzEVnKBXZGtR5nOWXkI8KRVpixWMr1kDQAErNwI/s93baexyjSnXz8osXyXUHvKsaeOWL5fA+/DDMiOG1lL9nZ2VkwVf9zpppWhokIA9MDB3e93dc6sXXr4srRp1dXJb2cKzNS6t5WexmEyHNz4u1fBHHpHbSCSktaOrS+57zRoZ74ED8v/mZmkBiUTmWkdCIQnWTU1SEddaKt7d3XI77e0yTmDhEuBeKLkdpNJtFXzfKwoDNBFVH54Yk1s1n3HfEZ5bQlyFZJ7utnUL+40b2rKHZ+s2qqQil68Sag95bW1S0c1cqru3V3qT6+qAxYuBn/xEqtP19RJUX3hBgrFVud27d65NwmrNiMWkj9q+CuGWLfL/tjbg8GEJs2Njcp+NjRLQY7H5LRUAsHmzXH58HHjqqbnVBIeH54d9peT2WlrkhMHDh6Wa3d8vt/ngg/L/VavmquNeKrkdhG0VgcAATUTVx6rghNqAyWFgeCDQQcgzld6x8COsJ2PzlxC3qndugrH1O+sEwIC+dvJVQguFvE2bgCeekEpvc7Msr93WJtXlhgYJqvYT+zJbIKzq98WLcp1Fi4A3vEHGAsi4hofl/2vXymwaV69Kj7VVFc68vXhcgvHsrITupiYZ55kzwLPPymqIgITpjo7599HZKaF8YEDCczwuLSD33FOWTV9aO0gV7cRVMwZoIjKf2yBmTVU2dli+P94rq+LV+gdRJQ8NexXWi3nuc1XvnB6qrpIjGNby1QcOyIl3bgPdpk3y78knga9/Xdopbr55fjtFrh7fSETC85kz8qcYi0mIX7JEWim6uyXMPvqohNzGRuB3fkeuu3z5wrFY1fTGRvmaSEhP9r59UnFuawPe+U4J0dbJjYDcR2/v3P0DC6vy1u07qRZXbHYNtlUYjwGaiMxWTJjpCAM3bwOO7gZaOqUqyemZKnto2IuwXuxzX2r1LoBTe9ln1LBaMYC51onBQfne/jsnM0VYcy6HQtK+8ZGPSHCNROZXtjODZVeXVJStaezq6oDVq4H//J/ldu1tIleuSNj+2tdkpo2VK+faLewtJ1bvcigkQXzLFqmMr1ghC6p8+9tSwT57dq41IxyWsG5vBenvnz+lndMZM2p6sRVagAGaiMyWGWaGB5yFo9XdwCv9Ep7ZRygqeWjYi7BebJAttXpXyth9aFuxgl3mwiJWr7F1ouCOHbJaoL0PudBMEVbl1zp576GH5DaAuRX9AOlPHh+X+7WmhfvQh4A//VMJ0TMzwPHjwOOPS2jetk2up5RMUXf5slwu17zOVo/1gw8CR4/K473rLplq79QpeQzWMuHT0zLdnbXMd2Y7hb11xc2MGTW72Apl5XuAVkp9BUA3gPNa6zf6PR4iMow9zOhZacdQqnBFstb7CHMFuUodGvZi+4dageQVmVUj25Rz5VLs2Cvc+mFVfU+fzr6wCDDXA51MSuXWCn/23+WaKSIaldvWWkLq5cty25kr+llzQNfXz5+dIxyWmTQuXZIAPTIi7Rkvvywn9bW3y/0kElKhtv5ZJxhmjunYMeAf/1Fu68UXgc99TnYEXnhhrj86kZCxWdPdZasSZwZqpzNmeL3YCgWb7wEawOMA/heAv/V5HERkInuYmTwNnHjceUWyVvsITenhLWX7j0VlFg0Vkinp3tRT2cdQzNgr2PphbyewKq9XrsjvrABq9RpbrR27dkn4s+ZqtuZSLnT78bgsjtLcLD3GiYQsXNLaKgHVCuSZurokVM/MyD7vzAzwyivyuyVLJFC/733A7bfPn7kj15gOHJAdgcZGGcOnPiUBXWu5XlPTXMjP159t52bGDC8XW6Hg8z1Aa61/oJRa6/c4iMhgVpgZi0pbBqd3yi+APbwL2OdtnjonrTimq1CPeTQqLQrj43OtFVNTUmFetQq49965JaqBua/r1s2dVPf443OrmScSwF/8hcyjvGmT/MzernD0qATgVauA8+elRSIel35oqx945Uq5HSu4W/f7/vfLnM6hkAToO+6QgPzyy3KZffvmTyVn9VzH4wv7oG+9VW5jclK+t1fU775bKuLWjsKpUzLOVttU4Lm4mTHDq8VWKPh8D9BUomqe05UoU623ZThVDfPIun0MJrwXevX6zPNYMvudlZKg2NIyV3W1WisyhcMSjBMJqdJeuiQh+upVuY0dO+RyViW4qUmCaDwu93PypLRYvP71wE9/Ki0TjY1yG7/3e1JJzqzM3nOPhOSJCQnXn/+8hPjdu+emlrNXifP1GV93nYR4q6daKQn3Vmi33+/OnRKwd+2SHQeGXvJaIAK0UupeAPcCwI033ujzaAxiymFaChYTgkYparUtw41q2NFw8xhMei8s9fWZ57FkVp6VkunpNm6ca88o1Jvb2irBe3Z2fr+0FYR37pQ5m5uaJPx+9rNyf4DMcLFypQTv8XG5/tSUzAu9fLkE+0z2BVbs4bq/f25qOft48/UZd3XJCYeJhNy31V6SKRaTx1COk/2i0SgikQi6uroQZiqvaYEI0FrrxwA8BgAbNmzQPg/HHNVwmJYqy6SgQeVVDTsaTh+Dm/dC03cgczyWbJXntra5mSbWrXPWmxuLSQhWCnj1VanSxuOy0qBS0rNsBc8jR+RnDQ1y3cZG4L77pI95715p5wAkeK9fL//PNk9yZttDtl5i+/Vy9Rnbr3f6tLShrF0rVXL7rBvFnOznJBhHo1Fs3boV8XgcTU1N6OvrY4iuYYEI0JRDNRympcriThdVI6fvhabuQNpDfY7HYp9Ozqo8W4ERcN6ba82nfOHCXDvGpUvZK9kbN8o0cSMjcl17f/O3vy3hu74eWLZMgnnmPMnZlge3ZFu10H69XKzrRaNSxT51ShZryZx1o69PWkVysQdmAI6CcSQSQTwex4oVK3Du3DlEIhEG6Brme4BWSvUDeAeApUqp0wB2aa2/7O+oAqIaDtNSZdXaTpfp1Ua7II3VNE7fC8u9A1nMc5gt1Gd5LPaqqr3yXEhmRdgeLq0V+vJVsq0TD4H5fcYPPyw90w0Nc1PO2fuXM+edzrfoSKHrWZfJrGr39Unlef/+7LNuWEt29/cDPT3HEIs9lzUwb9myxVEw7urqQlNTE86dO4fGxsb0bVFt8j1Aa623+D2GQKuGw7RUObW002VqtTGbII3VVE7eC8u5A1nsc5gt1N+0dcF1i5lCLdfKedlW6MvXbpHtvtatk9ANzA/WueadzteHbN85yLzewMBcEM4M4uGwjGFwcGG7xvxQPoWdO7+CRYu+mTUwy7gLB+NwOIy+vj5XPdDsma5evgdoqjGssvmvVna6TKw25sLWmsoo5w5ksc+hi1Dvdgq1QivnFTslW2Ywt09bZ4V8+7zThfqQ810PKPwYenpkjuiNG+cv/W2F8unpSYRCP84ZmLu7u9Hd3e2oBzrXZbL9rqieaX5GBgYDNFUOq2xUSSZWG/0YK81Xrh3IYp/DMoV6+yqCXq+cly+Y20O50xMb810PkAp0rsdgnzd6cHBuyrr5oXwEu3a9inPnEnkDc77gPDAwgN7eXiilFoThXEHZdc80PyMDhQGaKodVttridyUlM5gAwIk+MyvGQWqt8ft5NVUpz6HHod5eIQZkkZHMeZJL4XSWCy8WHcmsTkcicz8HnIb5dVi3bmHrhdMWjK1bt+L8+fMYGRnBbbfdhlgsNi8M5wrKrnum+RkZKAzQVDmsstUOUyop9hUMnY7HSUAsx2s5CK01pjyvpjLkOcwMlbkWVilWOZe0ztW3DWT/eWaYb22Noq9vYZtFOBxGOBxGNBpFX1+f455kKxx3dnZiZGQEw8PDWLZsWToMR6NRnD59GlrrBUHZdc80PyMDhQGaKidIVTYqjWmVFKfjcRoQvXgtu63kmlD5Ne15payKmQfZrXItaZ2ropy70hzFli0nAHRh/frL2LUrd89xMT3JVhU5Foth5cqVeNvb3oYtW7akw7h1ewBw9913o7u7O2twd4SfkYHCAE2VZUiFhsrMXknRs8DkaQmAfj33Tis7bgJiKa9lt5VcUyq/rJAFgpN5kMsh2yIqbuUK/9l+nhmI7bNrnDp1Cnv27MH27dsLtlrkEw6H0dPTg/7+fjz33HN48cUXMTQ0BAA4cOAAxsfHsWbNGpw7dw6dnZ2lz7TBz8jAYIAmIu9ZlZThAeB4L3DiceCVfn9bOZxUdioVEN1Wck2p/Aa1QmZC9d4H9nmQ883D7IV8rRf5rpNrfmcnP+/ri2Sdju7UqVM4c+YM9u/fj8HBwXSluZh5nKPRKHbt2jWvB/rSpUvYsWMHQqEQzp49C6UU2traCt4ep7SrLgzQRLWkkkGiIyz3pZT/wc8aT6H7LteJh5nb3W1Qd3L5Sj23flfIiml9MaF6X2GFprArVWb4dXt/+QJ3rvaQzJ9nBmJrdo09e/Zg//79WLp0KYaHhzEwMJBupbD3JANAX18fWltbEYvFsgbbbD3QoVAIoVAIa9asgVIKGzdunFfpzv54uQx4tWGAJqoVfgSJIB7yL+bEw3xy3U5mJXcsKhV7AFjdPf++ClV+ayUkFvM4TaneV1g5+6CzhV+395e5+uCePc5XV7TkOklv+/bteOaZZ3D48GEAQG9vb7o32X4y4datWzE+Po6zZ89i5cqVaG9vXxBs7T3Qa9euxbvf/W4AwL59+3Du3Dm0tbUVDM/yeLkMeLVhgCaqFX4EiaAe8ge8217W7YTagMlhCclWSLdubywKPLsZuHJSvj/eC9y5d2GILmaJ6mpqXyjmOQniTpwHyjlTRrZqc1cXsCW1rrB9yrxcfdFWR5nkbAAAIABJREFU4D51CjhzRpbjHhx032qS7SS9cDiMbdu2Yffu3ejs7Fww7Zw8Bgm0zc3NmJ2dRXNzMyYmJhb0TdtDemtrK3bt2pX3pMFcuAx49WGAJqoVfgUJvw/5F8ur7bW4S1azGJNqGI73Lqwwj0aA6XFA1cv3yQl3gT3XWKutMl3McxLknbgSlWumjIVTx2VfmbBQm0Zfn1Se9+8H1qwBTp2KYs+eCLZvL65H2N5j3N3djf7+fsRisayB1Qq0ExMTqKurw8jICEZGRvDUU09hcHAQPT0989o6rCBtryLnO2kws9+5mGXAyWwM0ES1ooaDRFG82l4dYeDmbcDR3UBLJ5CMLQzHi7uAhnYgMSLfh9rcBfZcY6229oVin5NcO3Hlqs5XU9U/i8zqttOp5wYG5lejw2Fp2xgclPB85sxW7N8fxzPPaGzbti1nddfpstnZAqu1qiCAdEgeGRlBT08PtNYYGRnB1atX8eEPfxjXXnvtvH5lp1XkXP3Obqa04wmH5mOAJqolQa0Ge81pwCm0vZzezupumYUkGcteOe0IS8tGrh5oJ7KNNcjtC7m2rVev4XJV56ut6o/cs2UAcysEFpp6bnYW6O2Vc4rt1ei5SnQE+/fHsXRpGw4fPozdu3ejv78/71zOWs8F7cwe44GBAXR2di4Iz5s3b8bJkycBAGvXrsXevXsRiUTQ3t6OWCyGq1evIh6Po76+fkH7h5MqcjQaxZ49e+ZNb5fZPlIoHD/55JPpWT6y9WWTGRigiai2eBFwrBP+jqcSQaHbcVI5LcfOTVCPOlQihJarOl9lVf9cbRhPPgns3AnU1wPt7UBPDxCL5Z567vRp4PHHcy+5vX17FwYHmzA8PAwABXuX29rmB22rgnz06FE0Njait7cXSql5FeBIJILx8XHU10ur1MTERLq3+erVq5iengYAhEIhaK3nrTpoD71bt27Nsa3mn5iYbXq7QrNxRKNR7Ny5E6+99hoaGxuhlEIktX45K9JmYYAmotpSasCxwt3UeWm56Lgte1tGJr+q/0E86lCJEFqu6nyQq/5ZZGvPAIAdO4DXXpOKs1JAfSyKrW9P7ahh7rmyqszRqMxHnWuWDqu6OzAwgN7e3oK9y5lB+/vf/z4uX76MmZkZzM7OQimVrgAPDAykg3JTUxMSiQQA4OrVq/jSl76E4eFhzMzMpAO31hrt7e248847sSV1ZuTmzZsxPj6O9vZ27N27N2uItcL90qVLEYvF8Ja3vAWf/OQns+4A5JqNIxKJoL6+Ho2NjZiensb09DRaW1s5BZ6BGKCJKBi86istNeBY4W5RpwToq8NA0zIzg1JQe3ErEULLVZ03uepfxOsh2/R0kQgQCsn309PATddF8c6WrUA09xEDJ7OCWG0SVktGtmprtqA9OzuL/v5+XLp0CY2NjVi8eDFmZmZw7tw5zM7OpqvRWmsAQFtbGy5fvozR0VEcPHgQALBu3bp0QK6vr0dzc3N61cG77roLJ0+eRH19PUZGRtLzSi/cVl3QWqenz7Mqx5mXyddH3dXVhfb2diilMDk5ife85z0YGhriFHgGYoAmIvN5eUi/1IBjhbtkDLhmrZwgWEzPcrkFuRe3UiG0XNV5E6v+Rb4ecgXf9napPE9PAw/+QQQtjYWPGDidFSTfyXZWK4W1aEokEsHp06fxl3/5l+mqbV1dHe6//34cOXIEzc3NePrpp9HW1oaXX34Zs7OzqKurw+zs7LzbvXjxIlauXIn169cDAH784x+jpaUFExMTOHPmTM5x2EO+k+nzCvVRZ+4gPP300+ngzynwzMIATUTm8/qQfikBx+QKo501NV59MzDtclo8E2Q+R0GtppuihL+hzOC7IFSv7gIGy9+2kq1/eOvWrYhGo+jv74dSCtPT07j//vvx5S9/OX2iYTwex09/+lMkk8l0GM3U2dmJ4eFhfPe73wUAzMzM4Pz586ivr8cdd9yBSCSCiYkJtLW1Yf369TlbKgpNnyfbL/sOgj2Ud3Z2QimVrjrffffdC06KJH8xQBOR+UzrKzWxwpgp1ApcPQvoWUDVyfdBFeRquik8/huaH6ors1OZq3/YXrUFgMnJyXmXW79+PU6fPo26ujrMzMxkve2XXnpp3vd1dXVYtmwZmpubcd1116Vn6+jq6sLAwADOnz+PJUuW4MKFC+n7tX5fzHzPmTsHPT09C5YpZ3A2CwM0EZnPxKqv6RXRZAxoWSkV6Jm4fB9UVTazhS/K/TdUgZ1Kq3/41KlT6ZPrrKpta2sr+vv701VnYK7l4dZbb8W//Mu/QGudM0BnqqurQ3Nzc3oWDfsS4L29vbh48SJee+01hEIhPProowtm/cg1U0cumTsHsViMC68YjgGaiILBpKpvECqi1uIsswmgweXCLKYx7QhEUJXrb6hCO5PhcBg9PT3YuXMnQqEQHnjgAQCAUgpXrlxBPB5HKBTCzMwM3vGOd+DNb34zuru7cezYMfT39yORSGBsbGxB/3NDQ0N6Cjvr9j74wQ+ioaEBGzduXDBLhlIKN9xwA1555RXccMMNmJqaQjwexy233DKvMm5ftKVQBTnbyYVuFl6hymOAJiJyKwgV0cyKIwCc6HMXckyosltjeFOPVNFNrfjXqjLuTGY7US8Wi2HRokVYsWIFjh49Cq01brnlFhw5cgTnz59PX/e73/0uhoaGsH79euzatQstLS1IJBK49tprMTExgWQyCUDCcnNzc7o/OhQKYcmSJRgYGIBSCs888wzWrVuXDsSnT59OV7gbGhoAAI2NjZiamsKpU6fSFevMRVt6e3vT09/lOgGx6IqzCX+nNYgB2g2+SIkICE5F1Ko4FhNyTKiymzAGyq+EnclcS3JbLRm7du1asOKgvVLb1tYGQFo1pqam5t32+Pg4JiYmcODAAcTjcaxZswanTp3C5OQkYrG5dqa6ujq0tLQgHo8jkUhgdnYWyWQS4+PjaGhoSE9bByDdowwA9957LxYtWoSDBw/iueeeQ0tLC5LJJHp6etJhONuiLceOHcu5ymBmxdnRct78G/ENA7RTfJESzZdth7JWdjJN7MnOp5iQ43WVvZjXRhAq/bXOyc5kluc+24wawFxIvXLlCkKhEJYuXYpIJII/+7M/S1dx7ZVaABgYGMDDDz+My5cvz7vb6elpbNy4EYODg+nA/cUvfhH9/f34zne+g8WLF+PKlSuYmJhAIpGAUgpKKaxfvx7PP/88kskkkskkotEoOjs70z3Kp06dwgsvvJBe2XBkZAS33XYbYrFYOpyPjIxgcnISiUQC9fX1aGtrQ2tr64JVBq1FXjJDcqEVC9P4N+IbBmin+CIlmpNthxKorZ1Mk3qyC8kMOaHWwu0cXlbZiy1AmF7pr8QOo+k7pYV2JnM895FIBBcvXoTWGnV1delFR+whNZlM4uTJk0gmk5iamsLJkycxMDCABx54YEFfclNTE5YvX47z58+jra0NHR0dePjhh7Fp0yYAwIEDB3DrrbciFovhjjvuwODgIBKJBC5fvozGxkYASH9961vfiqNHj+LChQsAgP7+fnR2dqZPYDxz5gyeeeYZjI2NYfny5ZidnZ237PeTTz6Jj3/84+k2kfe+97144IEHFqwyODk5mXXJcesxOVo8xfS/kSrGAO0UX6REc7LtUALcyfSK16HJHnJCrcCPdxUOs15W2YstQJhc6a/EUcmgHPnMtzNpPfehNlm1c3gA6AhjZGQEZ86cgdYaSimMjIzgrrvumtee0dPTg/7+fnzjG9/IOwVda2srzp49i9nZWTQ0NOCee+7BPffck+433rVrF8bHx9Hb24v29naMjo6mVytcsmQJVq1ahUgkgpaWFixfvhy/+Iu/iK985Svp208mk3jkkUfw2c9+FkeOHMFTTz2VnnP67NmzqK+vx/ve9770fe7ZswczMzNobW3F5OQkLly4gD179uDWW29NrzKYTCaxefNmfOtb30Jzc3O6xcMKyYVWLJy37U39G7GYvhNYJAZop4LwIiWqlFw7lNzJLF25QpMVck70OQ+zXlXZSylAmFrpr8RRyWo48rm4C9AaGJPlrXG8F1jdjSNHjsyrxh45cgQ7duxY0J7x5je/Gc899xwSiQTa2trQ3d294C6GhobQ0tKChoYGNDY24vbbb19QyW1ubsbMzAxGRkaQTCZx+fJlLFu2DEopxGIxrF69Gm9729uwZcsWDA0Noa6ubt59TE1N4aGHHsLHPvYx9Pb2pqvLK1euXHCfGzduRG9vLyYnJ6G1Ti/OUl9fj89//vO47rrr0NXVhWPHjuFLX/pSenXE1ta5udpdnVRo6t8IEJydwCIwQLth8ouUqJJy7VByJ7N05Q5NfhxNq8YCRCW2YzUc+ewIy3L3P9kNXFgCPD8CNA6kQ2YymUR9fT02btwIYO5EOnsPMADceeed2LJly4IgGY1G8eijj2JsbAxaazQ2NqaDqH3WjEQiAQDpivfs7CyUUnjkkUcwNDSE3t5e/PCHP8T3v/991NXVYXJyEvX19elw29TUhIaGBhw8eBBtbW2oq6vDxYsXEY/HsWTJknkV4k2bNuGJJ57AgQMHcPjwYRw8eBB1dXVIJBI4ePAgnnjiCQAS7leuXInm5mbE4/F5Jzfat0WgVcNOYA4M0GS2Kj30UxWy7VByJ7N05Q5NfoXZanttVGI7VsuOx+pu4Ae9wOdeBpIA9vdi0z/sTYfMjRs3pnuVLVbluK2tDSdOnMAPfvADDA0NpaeUs18uFoshFApBa41rr70WQ0NDGBoawqOPPpo+Ce++++7DokWL8NBDD0FrjWQyife85z1Yt24dhoaGMDIyglgslg7aK1euRDwex7ve9S5873vfg9Yak5OTePbZZzE2NpYO/vX19emZNyzRaBSxWAzbt2/Hl7/8ZQwODqaD+6pVq9KXa21txczMDCYmJhZUoEtmymdnNewE5sAATeaq4kM/RDlVKpjxb6l0ldiO1fBcdYSB+m1A/W6gsxO4FAMiEWzaunVBcLZYPcDDw8MAgM7OTsRisfSsFa2trYjFYhgZGcH4+Dimp6ehlEJDQwN6e3sxMjKCixcvoqmpKT1v844dO3DXXXdhYGAAvb29ePrpp7Fv3z7E43GMjo4imUwiFAohmUzi7NmzaGhowObNm7F582bs2LEDMzMzGB0dxfLly/Haa69hxYoVmJ2dxdDQUPpxZFuS+5vf/CYuX76Ma6+9Fvfcc0/6crt27cLMzAzOnz+P66+/Hrt27Vqwg1AUkz47q2UnMAsGaDJXFR/6IcqrGkITkd0d3UBrP3DmEjA9DRSotlo9wFbYjcVimJ2dRW9vLxKJBM6ePYuVK1diamoK11xzDa6//nrE43HceeedePHFF9HW1oYLFy6kWzXst2utJmhfjGXlypV49dVXF/Q2W20V11xzDVasWIHDhw8jHo+jrq4O586dQ11dHXp7e9MrDWZbktse+q3ZRqzLtbe348KFC2hvb0cikcg624aj+aDtTPvsrNL3MwZoMlcVH/ohIqop4TDQ0wPs3AmEQsCuXcC6dfLznFeRHuDu7m5EIhEcOnQITzzxRHrRklgshtHRUQDA5OQk1q5dmz4JMJFIoLGxEddeey2uu+66eScfZi7GEo/H8eqrr867b6u3ubW1FUNDQ9BaIxaLYe3atXj3u9+NI0eO4NChQ1i7di1isVg6+OZakhvAgsp0U1NTun3DalfJnG3D8XzQdvzsrAgGaDJXFR/6oYAypa+QKIhiMWDRImDFCuDcOSASkQAdjcr/u7qyBmorMH7605/GyMgIZmZmkEwmcenSJWit8brXvQ6Tk5PYtm0bNm3ahHXr1iESiWBkZAQHDx6c13ds3Z59houBgQF85jOfSVeb6+rqcNddd2HLli3p1RAB4O67704vDW6tdHjp0qV5wTfX7BnZKtPW5ax2lGwVZsfzQdvxs7MiGKDJbFV66IcCyKS+QqcY+MkkXV1AU5OE58ZG+T4aBbZuBeJx+V1fX9YQHYlEkEgksHr1aly4cAGhUAiLFy/Gq6++isnJSSxbtixdZQ6Hwzh27Bjuv/9+XLp0CXV1ddi3bx/27t2bc9ns3t5eHD9+HFprdHZ24pOf/OSC8Gr1YVtLgyulsHHjRmzfvn3ebWWbPSNXZbpQGHY8H3QmfnaWHQM0EZETpvUVFhLEwE/FCcqOUjgsAdlebe7rk/CcWZXOYF8sBQCWLFmCpqYm3Hzzzdi2bVu6BxmQtoedO3fiwoULmJmZQUNDA0ZGRhZUb+29xXv37sXAwAAAzLsta/XBZDKZXp5ba53+2caNGx31Jbua19mD61H5MUATETkRtL7CoAV+LwQlSHopCDtKmS0a9hCYrSqdRSwWmzdn8r333ovOzs6cbQ/19fUIhUKYmZnB9PQ0Ll++PG+aOHtvsdZ6QQgHJLz29PTgvvvuQzwex/3334/Vq1dDa42pqSm0tLTMmznD9cl+DlXFfNBViAGaiMiJoPUVBi3wlyoIQbIcTN9RKtSika0q/f+3d//BUd/3ncdfn5WQBAjGNmCDLSPHY9dO1aSaKRcm1+lcLm5CzqOWSd2OTWjrIcx4PMWhmUmm1GbuOC49O5Tp3GCOqeMZCtOLKjstyeDIjlX7PG1vSi81PhPqjcEm4GAB4YeFkGWMfqDP/fHmy3d3tavdr1ba7353n48ZZrXSd3c/3vVKr+9n35/3J4/Ozk4tbGrS6KVL13ckLBQqOzs7tXDhwutt7pYtWyZJ6uvrux52M/tMHz58WDt27NCePXsmBekjR47o4sWL1zdjcc5pZGREzjm1t7dfr0uWNOViv2ktBpz0VM5OQMf0EKABoFRJqitMWuAPTHcWudqD5GyZ7ROlIgv8ijp0qHiJRu6sdOZjXyur6Lj3XnVLOuS9OiV1HDt2/Wfq6sq6fW4LvLGxMZ0+fVovv/yyDhw4oO7u7kl9phctWqR3331XO3bsUE9Pz6SAm0ql5JzTxYsX1dLSMqkuudhiv2ktBsx6KsoP4JhZBGgAqFVJCvxSebPI9TbjHpjNE6USF/hNqcQSjbyP/cAD0nvv2fUbb1TH3LnquOce6eRJ6dFHpWst7PT009Jv/Ia0Zo10bUOTzBZ4u3bt0ssvv6zFixfr1KlT6u3t1aZNm7JC9sDAgKRww5ZDhw7p2LFjevPNN7Vo0SJJ0tjYmEZHR69v7f3www9PqpcutNhv2osBryk3gGPmEaABANWhnFnkpM64z4TZOlEqZfZYmnqWupQSjczbB4/7xhv2mM5JqZR09ar9O3tWGh+3rxsa7OvTp6W/+ztp/37pueeuh2h7+A5t2LBBr732mg4fPixJWRufBCE7d8OWvr4+Pf/889e34H7wwQf1yiuv6PLlyxofH1dzc7Pa2tqyunpMtdiv3MWA5QZwzDwCNACgOpQ7i5y0GfdqV8rs8VSz1JnBeO3a/I+ReXvv7XJ4WBoclCYm7N+cOdJNN0kbNkhvvy198pPSrl3S0JAFaMn6S4+MSD09dvuMsN7R0aF169Zpx44dWTPMkq4H2k2bNmUF6R/+8IcaHR29vtHK6dOnNXfuXDU1NWlsbEzj4+OTQmyxxX7lLAakG0f1IUAjuepxxT1QKXG8v+p5FrkalTJ7XGiWOjdYr19v4XfVqqwZ4qzbp9NWluGcBePGRvv6M5+xf7t22fUDB6Rt26QjR+w2zz9v9yFJP/6x9JOfTArzXV1d6unp0fDwsJqamtTa2pq3pjjY5rutrU2XLl3S5cuXNWfOHK1evVq7d++Wc05jY2N6+umnyw6xURcFFgzg/C2MBQEayVRrK+75BVhfqv31jvP9xSxydSm0wC9QaJa6t1c6d05qa5POnJG+8Q37/p492WUWnZ028/zOO3bpnF1mOnpUOn5cGhiQPv1pm2EeHpY2bbKfP/CA1NcntbRIP/pR3pKT3BncQjXFQanE6Oio2tvbtXLlSq1Zs0arV6/W8uXL1dfXp1WrVml15knANMzYosBa+1uYIARoJFMtrbjnF2B9ScLrXUvvr1JU8wlNuWOb7f+2fLPU6bQF5YEB+9fSYqG4tVW6fNnCbm4AHR21yyVLpLExm4kOgvSlS9I999h9nTplx2SWT6xebf/Saem11wqWnOTO4AY1xRMTE+rv71c6nS5YKpFOp69v633gwIHr7fCma8YWBdbbe7WKEKCRTLW04p5fgPUlCa93Nby/KhVqq/mEptyxlXv7UlvY5c5S9/ZaffLdd1vove8+6W//1sJzKmVlHMH9f+tbFnhHRqxsY9486atftZ8/95y0aJH07rt2P8uWSStXWreNfOMpsae0HZrd6m7v3r2T2tcFddKZfaNnqgvGjC0KrIb3ap0iQCOZaqlWkl+A9SUJr3eU99dsBN1KhtpqPqEpd2zl3D5qC7ugZ/PZs1aTfP68dOGCdOedVmoRlFkENdBBm7rjx23GOTA0ZLPXe/fabPLoqHTHHdL990svvWT1zUeO2LE5iwUlFS85yTgpyKx5zgzG0uRNUWa6C8aMLQqspb+FCUOARnLVSq0kvwCTYybCYlJe70Lvr8znQJqdoFvJUFvNJzTljq2c25fawk7K7tmc2WLOewu+x45lh+fg/gcGrOZ5zpwwRHtvHTj27bPQHmyWItmxS5daH+iNG222Okp/6jwnBfmCcb7Z5rVr1854F4wZ26K7Vv4WJgwBGqgG/AKsfjM5K5rU1zv3OWhfMztBt1jwC0J8Y6s0Ply7JzTljq2c20fZAOXQIZs5bmiw8CzZpXMWnv/yL+165gLC1larbR4dteMaG8OWdJL1dG5rs1nnoMWdZOMZGrLvLVxot58q3OeOM+ekoKNAMG5ubtbJkyc1Njam1tZWSTMYeFETCNAAUIpq/qi/UnKfA2l2Zm+nCn5BiB8bkj4+I81dJs1ZWLsnNOWObbq3j1BPrM5OC7MDA2HQbbwWL376U5tdbm62sBssIBwelm67zcLzhx9amcbrr4f3OTQkPfWU9X++5Ra77SOPWPDdudPCdjottbdPDveFarcLnBTkBuOOjg5t3bpVGzduVGNjo7Zs2VL2okHUHgI0qkM1r4IHpOr+qL9Scp+D27rs32y8dwsFvyDEN7RIfsIuJ0azT2j4fTIzitUTS2FY3bZN+sd/lP76r8NNUFIp66Zx9aotIJRsExQpDN2jo1bC8f77dvzEhP08+PriRQvYkpVsXLliX7e0WDBfuTJ7jFPVbkc4KRgeHta8efPYOhsFEaARv2peBQ8Eqvmj/kop9BxU8rkIQvzYh5JLSVdHpDkLwhMafp9UTm5YXbPGQvHly9LHH4d9nTNlzjKvWRN+vXNn9nFBkJ43L6yr3r5d+v3ft6/Hx+2+f/3Xs28XlJO0tFjwzi3vKOWkQGydjeII0IgfH40jKabzcXitzYbGXe6QGeLz1UDz+6RygpriBQtsAeE//ENYnxxsiPLBB9m3eeEFq2/etMmOXbjQZq9TKauhnjMnXFQ4f344+9zcbN8fHJRuvdXuO5WyEo9AOi298Yb1ipbs59fql6Ni62wUQ4BG/PhoHLWK2dDZMVWI5/fJ7MhXVxzsInjokM0Iv/qqfd97+9fUZEE4qIt2zmaGn3pK+tnPLOCeO2fXV62Svv99m3EOFhW2t9v230NDYYBetcq28h4dtVnq/n4bm2Sz4SdP2mPefLMF8OHh0vtZ52DRIKZCgEb8+GgctaqeZkPjnGnPfWx+n2QrFiBL+XlQquG9tG6d1NVlx65bJ33721abHJRa3HST1S7PmWPHBwsM582zy+Hh7I4b//qv9m/JEgvV3/ymtHu3dfC4cMGOGRuz+7nrrrC9XdAvuqfHykEuXLAZau9toeCiRfZ4UfpZAyUiQKM6xP2xMDAb6mU2NM6Z9kKPHffvk2op3Sm2IUopG6ZklmocPizt2GGhtbvbgvQzz9giwKCF3QcfhOUYIyNWhpFKWQgeH8+ekfbeZpvHxuxy/nwL4Fu3Sg8/bLPMwTEffWRjWbvWLoO+0GevdYS5ciWsu/beHnv79nA2u1g/ayCCVNwDcM59yTl31Dl3zDn3p3GPBwBmTDAb2rG5tss3Mmfag44Y9fDYhQShPv1ndjmYjm8smeH3/HmbuU2nLfwGM89Bb+Sgp3KuoP1bUFvc1pZ9bHOzzS6nUmH7OucsUC9YYMd7b7fx3kJ0Q4P9TApDbyoVtpc7ciTs3CHZbQYHw5rm3JZ0XV3Sli0W2p2zf3fcYdevXi2tnzUQQawz0M65Bkm7JH1BUr+k151zL3jvfxrnuABgxlTDbOhsi3OmvdzHjjpTXMrx1VS6E9QpHz5s1595xkofnLMAunVr8Q1TgvZvQdnEBx9YoG1tDWeC29ut5/PEhF0fH7cZ41QqLNcIOnI4J33lK1bPPDBgdc6f/KTNPA8MSLt2WZlHsLBwfNy+lqxVXrCFd25Luo4Oaflymx3/8Y/DAL91a/5tv4EyOB98lBLHgzv3WUn/1Xu/6tr1xyXJe/9UodusWLHCHzx4sEIjBACUpJpqoKPcLkrpSanHXz9u1EL9v++278f1/GzbZmUXbW02i+y9dM89Fpo3b7ZgWeoiu/37pa99zWaaFy6U1q+XnnzSQnWw+2BLi4XnYGfCpqYwWHtv4+jtnfxYTzwh/fmfh7PRixdb8A3a0l29anXNN9xQuByltzcs6bjllrBWG5gG59wb3vsV+X4Wdw30bZLez7jeL2ll7kHOuUckPSJJy5cvr8zIgHpTLTWbSKY4Z9qn+9i5M8Wneqd+D5Q6s5y7kFGKtxtLV5fNyg4Ph2UTmTPOmb2Riy0oHB62OuWlS63jxfbtVgIyNhYG5dZWC9CZ23qnUtJ990mf+1z+ULt/v4Xn4DYNDdLtt0u/9EvSj34UduZoacnaijtr3A88IB0/bjPWjY3SnXfaYwGzIO4A7fJ8b9KUuPf+WUnPSjYDPduDAuoO7dZQjzLLP/yEdPxaaUOwPwrfAAASZklEQVSh90CUcpHMUH+ie/olHTNxYpu7A5+UPyQHITToz7xv3+RjW1utNvnkyTCo3nijdd2YmAhrlTOlUvbvc5+z/s9BDXbmWL773TA8S/b1W29JBw9aYJ83T3r8cevOka/cJNhAJbNMJN9GKsAMiTtA90u6PeN6m6TTMY0FqF/VVLMJVErmTPHlfunE3qnfA9NtkTfdOu2ZPLHN3YEvX6js7bUNURoarBZ5927ptdfCDh1bt0pf/7qF5aYmW7S3e7cF1aYmW7A3Ph7uIhhobbW+zF1dk1viSTarfeZM9m2cs1lsyYLxxx9bcC+0FXewuDB4bO9ttp1Fg5glcQfo1yXd7Zz7hKRTkh6S9JV4hwTUoXpptwbkCmaKB9PSz3uKvwemUy4y3eAd94nt22/bRidtbRZyn3lG+vnPw5+fOBEG2tZWKxP5/vfDWeAlSyx4/9ZvSRs2hDPhQdePd96x0o+hoTD4plJ2mytXsscShO18W3Gn0xbmW1qsbvoLX7BjZqv+mXI3KOYA7b0fd849JqlPUoOkv/Lex9jvB6hTbD6Bejfb74HpBO9Kn9h2dVmXjWBG+cgRm4keGLCWcFK4hfbEhHT6dHagvesuC9NnzoSdM+bPt2Db22vHZLafW7BAunQpu3QjqKEOekZLdj8332xfp9OF+1QHvZ5XrbJZ7tlAuRuuibULx3TQhQMAUDcqPdsZdLJ4803bHXDxYuvc8eCD9vOdO+0ylZK+9z1p9ers2+/cKX3jG2HXjZtuspAsWQjPrKtubbW2dM8+G5ZrpFLSF78oHT1qt794UVq50sJ8UEry6KPZs8v799v3gl0Q9+2bvbrnE93W3zv4VKBjs/SJWQrriF01d+EAUGl8/AgkRxzdTXp6rKzizBkLsQsWSC+9ZF/ffLOF6l/9VZtxDuzfL/X1WVmH9xZ0R0as9KOhwY4JFvWtXWvbdAft8JqaLEAHbe6WLLHHHh21vs5LlkivvhruZrhtm/WK3rnTxrBpk23jHZSBBLPdsxGiKXfDNQRoIGnKCcB8/IipcHJVu0p9bTPLIZyzcoj2dmnvXgvSP/uZ1UUfPWoz1Pv2WRh+6CGbAQ52GgzKL1pbbQY62JK7tdVmuTdulH7xCwvPzc0Wshsa7JiODusG0tdnG6w8+WR4f5KF7Y8+svv4oz+yEpPgsc+fl/7iL6wUZd26ma+DptwN1xCggSQpNwDHvSgJ1YuTq9oV5bUNejifPGmBecMG+35PT7gJS2OjzQYHM8r//M8WYOfPtxnnefNss5NUSnrsMQvML7xg1zdtsjroYIOV0VG7v1tuscdZsEC6915bFDgyIr34ogXruXPDzh3j49bx4+OPreY5COeBVMq6iezYYePO3XClXPWwuyiKSsU9AAARZAbgiVG7HgUfP6KQcv/fQvUq9bUNulk0NlpI3bo1XCTY3W0zvm1tFlaDbbI7O22WuqHB2swFC/5aWuzrefOszvnyZZspPn7cWuOdP2+3CRYNLlhg979vn9U7nztn3wvC+rJlVt88f76NdWTE+k2/9JJ0//3hDLZkjyXZWEdHLeQH/33d3XYJlIkZaCBJyg3AfPyIQji5ql2lvra53SyGh8OfBUG6q8t6P58+La1ZE37/uees5GLVKjs+WNT35JMWbJuawhnk5uZw05VUSrr1Vnustja77Z49YfePZcuk3/1d+35Pj91HEJRvv91u39FhtdBB95Avf9mC9fBwuOFKvk1i2GAFZSBAA0kyEwGYjx+RDydXtavU1zazxVzuTn+Zgs1Vjhyx4NrRYd04go4c27ZZ94yGBlv0t3ixlWgMDdms8ZkzFqBvvdX6Sr/7rv28s9NCvHPS3Xfbz4aHbSvvwUF7zGB2PAjRwcLBbdvs2GCDlfXrszdc2bYte5OY3l4CNMpCgAaShgCM2cL/W7WrlNc2d8vvfAEzmKVeutSCdr6tss+etdln52yG+KGHpF/7Nam/X/rOd+z7779viwuds3rmQGurheUPPrDZ6itX7LGC685JixZJTzxhpRp79tgCR+9t0WAQ+vNtuCJZ4L561cYIlIEaaACVN5i2fqqD1CICVaWjw9rMFZqdLTZLnU6HLe/Gx60EY/16u8+uLiufaG6W7rxT+vznpdtus8dKpaw0ZOPGsNTjjjvs+6dO2eW991pLu69/3VrgtbWFbfaCRYNr1+avce7qsrGMj9ttXnqJWmiUhRloAJVFtwfMFNruVV6xWeqgBKOz04Lvo49mH7NmjV12ddnl2rVhJ42eHptpbmy0+7h82UL0/fdb4L161QJ0cNsgzJ86ZdeDLcfzzYp3dNhYduyY+jigRARoAJVFKz3MBE7E4lOoPEIKQ+3wcHbYTactLAe7CQb9mYMw3t9vG6MEm6XMm2e7H65fn7+mORhHd7fVM+/Zk71oMJ+uLgvpxY6LGyeGiUCABlBZdHuoHXH+oedErDoVmqEuVDsd/Nu/32afr161MouWFlusuH59eL8dHWEruuC+M7uDTFW7PdXYqgknholBgAZQWXR7qA1x/6HnRCwe6XRpQTX3Z8Vqp4eHrUZ5ZMR6QC9aFPZwDu4rdxY7c4OUqWbFi42tmnBimBgEaKAWJO0jP7o9JF/cf+g5Eau8qQJsMcVmfzs7bYHhhx9aDfTISLhRSzptZRpvvilduBAeV4s1zJwYJgYBGki6uGcCUTnVdKJUDX/oORGrrFJa2E0ls5wj83rwdRCwW1vDns6SbYDy3nthece5c9bPubV1Rv6zqgonholBgAaSLu6ZQFRG7onSp7ZK48Px/ZHlD339KXWjlULyzWBL2bPSuYG8u9s2YGlosNZ2DQ22OLGlJXunxFrCiWEiEKCBpKuGmUDMvswTpY9OSm98TWqcH++nDvyhry/lLsLLncHu7Q235y5UEhKUdgwMhAG6pSUs7wBiQoAGko6ZwPqQeaLkxyXXyKcOqLxyFuHlzmBLYaA+eVLatUvasGFyace+fRa2JdtMJXPLbiAmznsf9xgiWbFihT948GDcwwCAygtqoBtbpX/bIk2M2qcO1L2jWgRdOjLrmDODbmYXj2PHbEdB721x4LJlNtscZXEiMIucc29471fk+xkz0ACQFJklEwvu4lMHVJegxnloSDpzJn8gzuznvGWLddy4dMna1rW3T29xIhADAjQAJBH1x6g2QY1zS4ttzd3SMrmXc+6x7e1WvjE+Pv3FiUAMCNAAAKB8QY3zhx/altyZvZwLHXv2rB2zdSu1zUgUAjQAoLKqqZ81Zk6hXs75AnESttUGpkCABgBUDhv/1LYoXTqqfVttYAqpuAcAAKgjmf2sJ0btOqrbYFo60W2XACQxAw0AqCQ2/kkWPjEA8iJAAwAqh41/kiXzEwM27QGuI0ADACqLFnzJwScGQF4EaAAAkB+fGAB5EaABAEBhfGIATEIXDgAAACACAjQAAAAQAQEaAAAAiIAADQAAAERAgAYAAAAiIEADAAAAERCgAQDA1AbT0oluuwRAH2gAqAuDaTbDyMVzUprBtHRgrW3pnWq2jVV4vlDnCNAAUOsIQJPxnJTu4iF7nlqW2pbeFw/xXKHuUcIBALUuMwBNjNr1esdzUrobO+0k48pZKdVk14E6xww0ANQ6AtBkPCelu6HDZugpdwGuI0ADQK0jAE3GcxLNDR08R0AGAjQA1AMC0GQz+ZywIBGoKwRoAADKwYJEoO6wiBAAgHKwIBGoOwRoAADKwYJEoO5QwgHUA+ozgfJM9R5iQSJQdwjQQK2jPhMoTynvIRZpAnWFEg6g1lGfCZSH9xCAHARooNZRnwmUh/cQgByUcAC1jvpMoDy8hwDkIEAD9YD6TKA8vIcAZKCEAwCQDINp6US3XQJAjJiBBgBUP7rJAKgizEADAKofnTAAVJHYArRz7vecc2nn3IRzbkVc4wAAJACdMABUkThLON6S9DuSvhPjGAAASUAnDABVJLYA7b1/W5Kcc3ENAQCQJHTCAFAlqIEGAAAAIpjVGWjn3KuSlub50Wbv/f4I9/OIpEckafny5TM0OgAAACC6WQ3Q3vvfnKH7eVbSs5K0YsUKPxP3CQAAAEwHJRwAAABABHG2sfuyc65f0mclveic64trLAAAAECp4uzC8QNJP4jr8QEgdoPpeNuyxf34AJBQbOUNAHGIe2vquB8fABKMGmgAiEPcW1PH/fgAkGAEaACIQ9xbU8f9+ACQYJRwAEAc4t6aOu7HB4AEI0ADQFzi3po67sdH9WFhKVASAjQAAGBhKRABNdAAAICFpUAEBGgAAHINpqUT3XZZL1hYCpSMEg4AADLVaykDC0uBkhGgAQDIlFnKcOWsXa+XMMnCUqAklHAAAJCJUgYARTADDQBAJkoZgHgkqI0iARoAgFyUMgCVlbC1B5RwAAAAIF4Ja6NIgAYAAEC8Erb2gBIOAAAAxCthaw8I0AAAAIhfgtYeUMIBAAAARECABgAAACIgQAMAAAAREKABAACACAjQAAAAQAQEaAAAACACAjQA1IPBtHSi2y4BAGWhDzQA1LrBtHRgrW2Tm2q2zQoS0msVAKoRM9AAUOsuHrLw3LJUmhi16wCAaSNAA0Ctu7HTZp6vnJVSTXYdADBtlHAAQK27ocPKNi4esvBM+QYAlIUADQD14IYOgjMAzBBKOAAAAIAICNAAAABABARoAAAAIAICNAAAABABARoAAACIgAANAAAARECABgAAACIgQAMAAAAREKABAACACAjQAAAAQAQEaAAAACACAjQAAAAQAQEaAAAAiIAADQAAAERAgAYAAAAiIEADAAAAERCgAQAAgAic9z7uMUTinDsv6edxj6PCFku6EPcgEBmvW/LwmiUPr1ky8bolTz2+Zu3e+yX5fpC4AF2PnHMHvfcr4h4HouF1Sx5es+ThNUsmXrfk4TXLRgkHAAAAEAEBGgAAAIiAAJ0Mz8Y9AEwLr1vy8JolD69ZMvG6JQ+vWQZqoAEAAIAImIEGAAAAIiBAJ4xz7pvOOe+cWxz3WDA159y3nHOHnXOHnHN/75y7Ne4xoTjn3Hbn3JFrr90PnHM3xD0mTM0593vOubRzbsI5R5eAKuac+5Jz7qhz7phz7k/jHg+Kc879lXPunHPurbjHUk0I0AninLtd0hcknYx7LCjJdu/9p733nZJ6Jf2XuAeEkrwi6Ve895+W9I6kx2MeD4p7S9LvSPqnuAeCwpxzDZJ2SfpPkn5Z0hrn3C/HOyqUYK+kL8U9iGpDgE6W/yHpTyRRuJ4A3vuhjKvzxeuWCN77v/fej1+7+n8ltcU5HhTnvX/be3807nGgqM9IOua9P+69H5X0nKTVMY8JRXjv/0nSQNzjqDaNcQ8ApXHO/bakU977nzjn4h4OSuSc+++S/lDSJUn/MebhILqvSno+7kEANeI2Se9nXO+XtDKmsQBlIUBXEefcq5KW5vnRZklPSPpiZUeEYqZ6zbz3+733myVtds49LukxSVsqOkDkVex1u3bMZknjkrorOTbkV8prhqqXb/aHT+aQSAToKuK9/81833fOfUrSJyQFs89tkv6fc+4z3vtfVHCIyFHoNcvjbyS9KAJ0VSj2ujnnHpbUJek+T6/PqhDhvYbq1S/p9ozrbZJOxzQWoCwE6ATw3v+bpJuD68659ySt8N5fiG1QKMo5d7f3/t1rV39b0pE4x4PSOOe+JGmTpP/gvb8c93iAGvK6pLudc5+QdErSQ5K+Eu+QgOlhESEwe77tnHvLOXdYVn7zx3EPCCX5n5IWSHrlWgvCZ+IeEKbmnPuyc65f0mclveic64t7TJjs2uLcxyT1SXpb0ve89+l4R4VinHM9kv5F0j3OuX7n3Pq4x1QN2IkQAAAAiIAZaAAAACACAjQAAAAQAQEaAAAAiIAADQAAAERAgAYAAAAiIEADAAAAERCgAaCOOOdeds4NOud64x4LACQVARoA6st2SX8Q9yAAIMkI0ACQcM65f+ecO+yca3HOzXfOpZ1zv5LvWO/9/5b0YYWHCAA1pTHuAQAAyuO9f90594KkP5M0V9J3vfdvxTwsAKhZBGgAqA3/TdLrkq5I2hjzWACgplHCAQC14SZJrZIWSGqJeSwAUNMI0ABQG56V9J8ldUvaFvNYAKCmUcIBAAnnnPtDSePe+79xzjVIOuCc+7z3/rU8x/4fSfdKanXO9Uta773vq/CQASDRnPc+7jEAAAAAiUEJBwAAABABJRwAUGOcc5+S9L9yvj3ivV8Zx3gAoNZQwgEAAABEQAkHAAAAEAEBGgAAAIiAAA0AAABEQIAGAAAAIiBAAwAAABH8f3CV0+3se8vUAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for t in range(NUM_TRIALS):\n",
    "       # main(is_semi_supervised=False, trial_num=t)\n",
    "\n",
    "        # *** START CODE HERE ***\n",
    "        # Once you've implemented the semi-supervised version,\n",
    "        # uncomment the following line.\n",
    "        # You do not need to add any other lines in this code block.\n",
    "     main(is_semi_supervised=True, trial_num=t)\n",
    "        # *** END CODE HERE ***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## (f) Comparison of Unsupervised and Semi-supervised EM"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**i. Number of iterations taken to converge**\n",
    "\n",
    "The unsupervised model takes longer to converge: About 120-170 iterations without supervision vs. about 25 Iterations with supervision."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**ii. Stability (i.e., how much did assignments change with di\u000b",
    "erent random initializations?)**\n",
    "\n",
    "Due to having no observed data to base its classifications on, it is to be expected that the unsupervised model does not label any data point consistently (i.e. there is no point that always gets colored the same independent of initialization). The semi-supervised model does not have this problem, because it knows the correct labels of at least some examples.\n",
    "\n",
    "But furthermore the unsupervised model even fails to create comparable partitions of the dataset, while the semi-supervised model seems to always end up with the same partition."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**iii. Overall quality of assignments.**\n",
    "\n",
    "The unsupervised model seems to have trouble to identify the high-variance  distribuition and to distinguish two of the low-variance distributions. The semi-supervised model does seem to find reasonable assignments everytime."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
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   "file_extension": ".py",
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   "nbconvert_exporter": "python",
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